UC-NRLF 


SB    EM2 


PHYSICAL  LABORATORY 
GUIDE 


FREDERICK  C.  REEVE 


GIFT  OF 


PHYSICAL  LABORATORY 
GUIDE 


BY 
FREDERICK   C.   REEVE,  E.E. 

MASTER   IN   PHYSICS,   NEWARK   ACADEMY,   NEWARK,    NEW  JERSEY 


***    •    •     J  V  **"*'•*»•*•>•*  *"> 


NEW  YORK  •:•  CINCINNATI  •:•  CHICAGO 

AMERICAN    BOOK    COMPANY 


(Vt 


COPYRIGHT,  1912,  BY 
FREDERICK  C.   REEVE. 


COPYRIGHT,  1912,  IN  GREAT  BRITAIN. 


REEVE  S    PHYSICAL   LABORATORY   GUIDE. 

w.  P.    i 


'»  / 

••I-  •  •    * 


PREFACE 

I  HAVE  endeavored  to  prepare  a  book  which  shall  inspire 
in  the  pupil  the  spirit  of  inquiry  and  comparison  towards 
his  laboratory  work.  This  appeals  to  me  as  the  sanest 
and  most  rapid  way  by  which  to  lead  the  beginner  in  sci- 
ence to  a  knowledge  of  its  fundamental  principles. 

The  experiments  chosen  for  this  book  are  almost  en- 
tirely quantitative.  Twelve  years'  experience  has  taught 
me  to  use  quantitative  experiments  in  the  laboratory  and 
those  of  a  purely  qualitative  nature  in  demonstrations  in 
the  class  room,  as  far  as  possible. 

Again,  the  working  directions  in  this  manual  are  un- 
usually full.  The  delusion  of  giving  the  pupil  only  a  hint 
about  the  experiment  and  then  expecting  him  to  work  it 
out  for  himself  always  results  in  confusion  on  the  part  of 
the  pupil  and  an  impossible  situation  for  the  teacher.  The 
pupil  must  have  directions  as  to  the  main  steps  in  the  ex- 
periment. It  is  simpler  to  print  these  than  to  expect  the 
teacher  to  give  them  over  and  over  to  each  pupil. 

Attention  is  also  called  to  the  large  number  of  questions 
scattered  through  the  text.  If  the  teacher  will  insist  that 
the  pupil's  record  contains  the  pupil's  answers  to  these 
questions,  they  will  be  a  great  help  in  enabling  him  to  un- 
derstand and  remember  the  fundamental  principles  which 
each  experiment  teaches. 

Another  feature  of  this  manual  is  the  reference  notes. 
These  include  important  fundamental  laws  and  definitions 

iii 

251955 


iv  PREFACE 

referred  to  in  the  text.  Pupils  always  forget  and  should 
be  taught  to  refresh  their  minds  constantly  by  the  use  of 
works  of  reference. 

The  tables  of  numerical  data  are  full  and  carefully  pre- 
pared and  will  be  found  useful. 

A  few  pieces  of  home-made  apparatus  are  also  described. 
These  are  inexpensive  and  require  very  little  skill  to  make. 

Finally,  this  manual  covers  all  the  requirements  of  the 
"  College  Entrance  "  and  other  Examination  Boards.  Its 
wide  range  of  subjects  makes  it  possible  to  prepare  from 
its  pages  courses  to  suit  any  requirement. 

I  wish  to  acknowledge  the  helpful  suggestions  and  criti- 
cisms of  my  associates  and  particularly  the  services  ren- 
dered by  my  brother,  Henry  M.  Reeve,  A.B.,  in  reading 

the  proof. 

FREDERICK    C.    REEVE. 


HINTS  FOR  THE  LABORATORY 
RECORD 

IT  will  be  well  to  have  the  pupils  familiarize  themselves 
with  the  following  plan  before  starting  the  laboratory 
work. 

The  record  of  each  experiment  should  have  the  following 
parts : 

1.  The  Date. 

2.  The  Experiment  Number. 

3.  The  Object. 

4.  The  Numerical  Data. 

5.  The  Description. 

6.  The  Conclusion. 

It  will  be  found  convenient  to  use  a  notebook  bound  on 
the  side  in  such  a  manner  that  the  pages  of  the  open  book 
will  lie  flat  upon  the  table. 

Begin  your  record  on  the  left-hand  page  by  placing  the 
date  (day,  month,  and  year)  in  the  upper  right-hand  corner. 
Place  the  experiment  number  in  the  center  of  the  page 
about  an  inch  below  the  top.  Copy  the  object  given  by 
\\\Q  guide  directly  below  the  number,  heading  it  Object,  in 
the  margin. 

Place  the  table  for  numerical  data  just  a  little  below  the 
object.  This  should  be  accurately  laid  out  with  a  ruler 
and  made  large  enough  to  hold  the  pupil's,  handwriting 
without  crowding.  Mark  this  table  Data,  in  the  margin. 

Under  the  heading  Description,  also  in  the  margin,  write 
a  complete  record  of  everything  you  did  of  importance  in 
connection  with  the  experiment. 

A  simple  rule  to  follow  is  to  put  down  the  various  steps 
in  the  experiment  in  the  exact  order  in  which  you  did 
them. 


vi  HINTS   FOR   THE   LABORATORY    RECORD 

Remember  that  your  readers  will  not  have  the  Laboratory 
Manual  or  any  other  guide  at  hand  when  they  read  your 
record ;  it  should  therefore  be  complete  by  itself. 

Finally  write  the  conclusion,  placing  its  heading  in  the 
margin.  This  should  include  your  result  in  concise  form, 
together  with  a  clear  and  careful  statement  of  any  funda- 
mental laws  or  principles  to  which  the  experiment  may 
lead. 

It  is  well  to  write  upon  but  one  side  of  the  leaves.  This 
will  enable  you  to  remove  a  leaf  without  disturbing  a 
previously  completed  record. 

Remember  that  the  original  record  made  in  the  labora- 
tory is  the  one  to  be  preserved.  Therefore  take  pains  to 
have  it  accurate,  neat,  and  well  laid  out. 

When  time  permits,  one  laboratory  period  a  month  should 
be  devoted  to  an  informal  discussion  of  the  experiments  per- 
formed that  month.  If  several  of  the  pupils'  records  are 
read  and  then  criticized,  first  by  the  other  pupils  and  then 
by  the  instructor,  a  valuable  review  of  the  work  will  be 
made,  and,  in  addition,  interest  and  friendly  rivalry  will  be 
gained,  which  will  greatly  improve  the  pupils'  records. 

The  experiment  to  be  performed  each  laboratory  period 
should  be  assigned  in  advance,  and  the  pupil  required  to 
study  carefully  the  record  of  that  experiment  given  in  this 
guide.  This  will  effect  a  great  saving  in  time,  and  the 
pupil  will  go  about  his  work  much  more  intelligently. 

In  performing  the  experiment  and  in  writing  the  record, 
never  lose  sight  of  the  real  objects  of  your  work  in  the 
laboratory : 

1.  To  increase  your  knowledge  of  physics. 

2.  To  train  your  hands  for  the  delicate  manipulation  of 
various  kinds  of  apparatus  and  many  other  things. 

3.  To  form  the  habit  of  careful  and  accurate  observation. 

4.  To  gain  the  ability  to  record  the  results  of  your  work 
in  clear  and  logical  fashion. 


CONTENTS 


CHAPTER   I 
FUNDAMENTAL  MEASUREMENTS 

EXPERIMENT  J'AGK 

1.  To  find  the  volume  of  a  rectangular  block  i 

2.  To  test  the  right-angled  triangle  relation       ....  3 

3.  The  use  of  the  micrometer  caliper          .....  4 

4.  A  lesson  on  the  use  of  a  scalepan  balance      ....  5 

5.  The  use  of  the  graph  in  recording  results       ....  7 

6.  To  calibrate  a  spring  balance.     The  graph  applied        .         .  9 


CHAPTER   II 

DENSITY  AND   SPECIFIC   GRAVITY 

7.  To  test  Archimedes1  principle        .         .         .         .         .         .n 

8.  To  test  the  law  of  flotation    .         .         .         .         .         .         .12 

9.  To  find  the  volume  of  an  irregular  solid         .         .         .         .13 

10.  Density  of  a  solid  heavier  than  water    .         .         .         .         .14 

11.  Density  of  a  solid  lighter  than  water 15 

12.  Density  of  a  solid  soluble  in  water         .....  16 

13.  Density  of  a  liquid.     Bottle  method      .         .         .         .         .  17 

14.  Density  of  a  liquid.     Fahrenheit  hydrometer  18 

15.  Density  of  a  liquid.     Displacement  method  ....  20 

16.  Density  of  a  liquid.     Balancing  columns       ....  21 

CHAPTER  III 

MAGNETISM 

17.  Field  about  a  bar  magnet.     Compass  method        .  *      .         -23 

18.  Plotting  several  fields  with  iron  filings 24 


viii  CONTENTS 

EXPERIMENT  PAGE 

19.  Magnetic  field  about  a  single  conductor         ....       25 

20.  Magnetic  field  about  a  galvanoscope  28 

CHAPTER    IV 

VOLTAIC  CELLS  AND  THERMOCURRENTS 

21.  Study  of  a  simple  voltaic  cell         ......  30 

22.  Study  of  a  Daniell  cell.     (Method  i) 32 

Study  of  a  Daniell  cell.     (Method  2)     .         .         .         .         •  33 

23.  Thermocurrents  from  iron  and  copper  34 

CHAPTER  V 

ELECTRICAL  TESTING 

24.  Method  of  handling  a  galvanometer.     (Parti)  37 
Relation  between  resistance  and  deflection.     (Part  2)  .         -39 

25.  Resistance  of  a  conductor.     Substitution  method  .         .       40 

26.  The  e.m.f.  of  a  cell.     Equal  deflection  method      ...       42 

27.  Resistance  of  a  conductor.     Wheatstone  bridge     ...       44 

28.  Resistance  of  a  cell.     Method  of  opposition  .         ...       47 

29.  Resistance  of  a  cell.     Mance's  method 48 

30.  Resistance  of  a  cell.     Half-current  method    ....       50 

31.  Testing  the  laws  of  resistance .       52 

32.  The  temperature  coefficient  of  copper    .         ...         .         -53 

33.  Counter  e.m.f.  of  a  motor.     Resistance:  Fall  of  potential 

,        method      .         .         .         .         .         .         .         .         .         -55 

34.  Construction  and  control  of  a  motor 56 

35.  A  study  of  the  direct  current  dynamo 58 

CHAPTER   VI 

MECHANICS   OF   SOLIDS 

36.  The  laws  of  beams.     (Parti) 60 

Plotting  curves  to  show  these  laws.     (Part  2)  .         .62 

37.  To  test  the  parallelogram  law        .         .         .         .         .         .63 

38.  To  test  the  laws  of  parallel  forces  .         .         .         .         «         .       65 

39.  Center  of  gravity  and  weight  of  a  lever .         ,        .         .         .67 


CONTENTS  ix 


EXPERIMENT 

40.    To  test  the  laws  of  vibration  of  a  pendulum  .... 

PAGE 

69 

41. 

To  find  the  breaking  strength  of  a  wire          .... 

70 

42. 

The  elastic  limit  and  "  modulus  of  elasticity  "  of  steel    . 

73 

AT.. 

7C 

T-J 

44- 

To  plot  the  path  of  a  projectile  on  section  paper    . 

/  } 
76 

45- 

To  test  Boyle's  law        V'  .     . 

78 

CHAPTER   VII 

HEAT 

46. 

Freezing  point  and  boiling  point  of  a  thermometer        .        . 

80 

47- 

Variation  of  boiling  point  with  pressure         .... 

82 

48. 

The  coefficient  of  linear  expansion  of  brass    . 

83 

49- 

Measurement  of  quantity  of  heat.     "  Method  of  Mixtures  "    . 

85 

50. 

The  specific  heat  of  a  solid    .         .         .         .         .     ...»    ,    .,. 

86 

51- 

The  latent  heat  of  fusion  of  ice      . 

88 

52. 

The  latent  heat  of  vaporization  of  steam         . 

90 

53- 

Dew  point  and  per  cent  of  humidity      .         .         .         .         «. 

91 

CHAPTER   VIII 

LIGHT 

54- 

The  candle  power  of  a  lamp.     Rumford  photometer 

94 

55- 

The  candle  power  of  a  lamp.     Bunsen  photometer 

95 

56. 

Position  and  kind  of  image  in  a  plane  mirror 

96 

57- 

The  index  of  refraction  from  air  to  glass        .... 

98 

58. 

The  index  of  refraction  from  air  to  water       .... 

99 

en. 

IOI 

jy 

60. 

The  lens  formula  —  =  —  +  —  •     Conjugate  foci  . 
F     Do     Di 

102 

61. 

The  spectroscope           .         .         .         .         .  '      .       •  .         . 

103 

i 

CHAPTER    IX 

SOUND 

62. 

To  plot  several  wave  motions  on  section  paper 

I05 

63- 

To  measure  the  vibrations  of  a  tuning  fork    .... 

107 

X  CONTENTS 

EXPERIMENT  PAGE 

64.  Resonating  air  columns.     Their  relation  to  wave  lengths       .  109 

65.  To  test  the  law  of  strings no 

66.  To  find  the  velocity  of  sound  in  air 113 


CHAPTER   X 
NOTES   ON   THE   EXPERIMENTS 

FVNDAMENTAL   MEASUREMENTS    (CHAPTER   I)    .  .  .  .115 

DENSITY  AND  SPECIFIC  GRAVITY  (CHAPTER  II)       .        .^     .     119 

VOLTAIC  CELLS  AND  THERMOCURRENTS  ;  ELECTRICAL  TESTING 

(CHAPTERS  IV  AND  V) 123 

THE  MECHANICS  OF  SOLIDS  (CHAPTER  VI)      .        .        «        .  131 

HEAT  (CHAPTER  VII)        .  140 

LIGHT  (CHAPTER  VIII)     r 142 

SOUND  (CHAPTER  IX) 144 

CHAPTER   XI 
TABLES  OF  PHYSICAL  CONSTANTS 147 

CHAPTER   XII 

APPARATUS    REQUIRED    FOR  THIS    BOOK  AND   SOME  USEFUL 

HOME-MADE  APPARATUS -175 


PHYSICAL  LABORATORY  GUIDE 


CHAPTER  I 

FUNDAMENTAL   MEASUREMENTS 

EXPERIMENT  1 
Object.  —  To  find  the  volume  of  a  rectangular  block. 

Apparatus.  —  A  weighted  rectangular  block,     a  2O-cm. 
scale,  a  5oo-c.c.  graduate,  and  a  piece  of  thread. 


Data.  — 


METHOD  i.    (By  CALCULATION) 


OBSERVATIONS 

TRIAL  i 

TRIAL  2 

AVERAGE 

Length      

Width        

Thickness       ..... 
Volume 

METHOD  2.     (By  DISPLACEMENT) 

OBSERVATIONS 

TRIAL  i 

TRIAL  2 

AVERAGE 

Volume  of  water 
Volume  of  water  and  block 
Volume  of  block 

• 

Directions,  Method   i. — To  measure  the  length  of  the 
block,  place  the  metric  scale  parallel  with  one  of  its  edges 


LABORATORY   GUIDE 

and  in  such  a  position  that  the  graduations  are  in  contact 
with  the  block.  One  end  of  the  block  should  coincide  with 
some  convenient  mark  on  the  scale.  The  zero  mark  should 
be  avoided  if  the  divisions  near  it  are  worn.  Now  count 
the  centimeters  contained  in  the  length  of  the  block,  also 
the  additional  tenths  of  centimeters  (millimeters)  and  esti- 
mate the  tenths  of  millimeters,  writing  these  as  hundredth 
parts  of  a  centimeter.  You  will  now  have  the  length  of 
the  block  in  centimeters,  accurate  to  the  one  hundredth 
part  of  a  centimeter  if  the  work  has  been  carefully  done. 
Record  this  in  the  table. 

For  Trial  2,  measure  the  length  of  the  block  on  the 
opposite  side,  using  a  different  part  of  your  scale.  This 
will  average  any  irregularities  in  either  the  block  or  the 
scale  and  increase  the  accuracy  of  your  work.  Measure 
the  width  and  thickness  of  the  block  in  the  same  manner. 

Find  the  average  length,  width,  and  thickness,  and  from 
these  calculate  the  volume  of  the  block. 

Directions,  Method  2.  —  Fill  the  graduate  about  half  full 
of  water  and  read  its  volume,  estimating  tenths  of  the 
smallest  divisions. 

It  will  be  observed  that  capillary  action  causes  the  water 
to  be  drawn  upward  against  the  sides  of  the  glass,  giving 
the  water  the  appearance  of  having  two  surfaces  ;  the  lower 
of  the  two  is  evidently  the  true  surface.  Its  position  against 
the  scale  of  the  graduate  is  the  one  that  should  be 
measured.  Now  lower  the  block  into  the  graduate  by  means 
of  the  thread  and  again  read  the 'position  of  the  surface 
of  the  water. 

For  Trial  2,  start  with  a  different  quantity  of  water  in 
the  graduate  and  proceed  as  before. 

From  these  readings  calculate  the  volume  of  the  block. 


FUNDAMENTAL   MEASUREMENTS  3 

The  Pupil's  Aim.  —  In  this  experiment  particular  effort 
should  be  made  to  gain  proficiency  in  estimating  tenths  of 
the  smallest  divisions  of  the  scales  used.  Keep  in  mind 
that  the  smallest  part  of  a  space  which  you  can  read  may 
be  called  one  tenth ;  a  scant  quarter,  two  tenths ;  a  big 
quarter,  three  tenths ;  a  small  half,  four  tenths  ;  etc. 

This  process  of  estimating  tenths  will  be  used  in  all  sub- 
sequent work.  Its  importance  cannot  be  overestimated. 

Conclusion.  —  i.  Explain  any  difference  in  results  given 
by  the  two  methods. 

2.    How  would  you  find  the  volume  of  an  irregular  solid  ? 


EXPERIMENT  2 

Object.  —  To  test  the  relation  between  the  arms  and  the 
hypotenuse  of  a  right-angled  triangle. 

Apparatus.  —  A    small    draughtsman's    triangle    and    a 
2O-cm.  scale. 

Data.  — 


LENGTH  OF 

ARM  i 

ARM  2 

HYPOTENUSE 

Trial  I 

Trial  2 

Average 

(Average)2     
Error    

Directions.  —  Measure  the  three  sides  of  the  triangle  in 
centimeters.  Follow  the  directions  for  measuring  given  in 
Experiment  i.  As  this  experiment  is  a  test  of  your  ability 
to  estimate  tenths  of  millimeters,  special  attention  should 


4  PHYSICAL   LABORATORY   GUIDE 

be  given  to  this  point.  Average  the  lengths  found  in 
Trials  I  and  2  and  square  the  results.  Add  the  square 
of  arm  I  to  the  square  of  arm  2  and  compare  this  sum 
with  the  square  of  the  Hypotenuse. 

Conclusion.  —  State  the  true  relation  between  the  arms 
and  the  hypotenuse  of  any  right-angled  triangle.  What 
is  the  probable  cause  of  your  error  ? 

EXPERIMENT  3 

Object.  —  To  measure  several  small  objects  with  a  mi- 
crometer caliper. 

Apparatus.  —  A  micrometer  caliper,  pieces  of  wire  and 
sheet  metal,  and  a  ruler. 

Data.  — 


OBJECT  TO  BE  MEASURED 

TRIAL  i 

TRIAL  2 

AVERAGE 

Directions.  —  The  micrometer  caliper  applies  the  prin- 
ciple of  the  screw,  one  of  the  six  simple  machines.  The 
pitch  of  the  screw  is  made  some  convenient  size,  such  as 
.025  of  an  inch.  If  the'  scale  on  the  movable  sleeve  is 
divided  into  twenty-five  parts,  the  instrument  reads  thou- 
sandths of  an  inch  directly,  and  ten-thousandths  may  be 
obtained,  with  a  fair  degree  of  accuracy,  by  estimating 
tenths  of  these  smallest  divisions. 


FUNDAMENTAL  MEASUREMENTS          5 

The  smallest  spaces  on  the  fixed  scale  are  each  one 
revolution,  and  consequently  have  a  value  of  twenty- 
five  one-thousandths  of  an  inch.  A  group  of  four  of 
these  will  therefore  have  a  value  of  one  tenth  of  an 
inch. 

To  make  a  measurement,  close  the  instrument  upon  the 
object,  using  the  greatest  care  to  insure  that  the  jaws  of 
the  caliper  touch  the  object  lightly  and  no  more.  The  use 
of  any  pressure  would  change  the  size  of  the  object,  or 
injure  the  micrometer,  or  possibly  both,  besides  giving  an 
incorrect  measurement. 

Read  the  whole  spaces  on  the  stationary  scale,  and 
the  whole  divisions  on  the  movable  sleeve  and  estimate 
the  value  of  a  fractional  part  of  one  of  these  spaces 
to  the  nearest  tenth.  The  sum  of  these  readings  with 
their  proper  values  assigned  is  the  required  size  of  the 
object. 

Make  two  or  more  trials  for  each  object  measured  and 
record  these  trials  and  the  average  value  obtained  from 
them. 

Conclusion.  —  Give  two  reasons  why  several  trials  are 
desirable.  If  you  have  just  used  a  micrometer  reading  in 
the  English  system,  suggest  a  convenient  pitch  and 
arrangement  of  scales  for  such  an  instrument  to  read  in 
the  Metric  system,  or  vice  versa. 

EXPERIMENT  4 
Object.  —  To  make  a  weighing  with  a  scalepan  balance. 

Apparatus.  —  A  scalepan  balance,  a  set  of  weights, 
500  gm.  to  10  mg.,  several  small  objects  of  various 
weights. 


PHYSICAL    LABORATORY   GUIDE 


Data.  — 


NAME  OF  OBJECT 

SUM  OF 
GRAM 
WEIGHTS 

SUM  OF 
MILLIGRAM 
WEIGHTS 

COMPLETE 
WEIGHT 

Directions.  —  (i)  Be  sure  that  the  balance  is  true  before 
using  it.  This  is  easily  determined  by  allowing  it  to  swing 
through  a  small  arc.  If  true,  the  vertical  index  will  swing 
through  equal  arcs  on  either  side  of  its  vertical  position. 
Make  any  necessary  adjustment.  If  no  other  means  is 
provided,  add  a  small  piece  of  paper  to  the  light  scalepan, 
adjusting  its  size  until  the  balance  is  perfectly  true. 

(2)  Never  handle  any  weights  with  your  fingers.     Use 
the  tweezers  provided  for  the  purpose.     Contact  with  the 
moisture  of  the  hand  corrodes  the  weights. 

(3)  Try  all   the  weights   in  order,  beginning   with   the 
heaviest  one  which  you  think  will  be  required.     Following 
this  simple  rule  will  give  rapid  and  accurate  results. 

(4)  There  are  only  two    places   for   the  weights  while 
making  a  weighing:  (a)  in  the  scalepan  of  the  balance; 
(^)'on  the  block  provided  for  the  purpose.     After  adjust- 
ing the  balance  with  the  object  in  one  of  the  scalepans, 
count  the  weights  in  the  other  pan,  adding  the  whole  gram 
and  milligram  weights  separately.     Record  these  results. 
Now  divide  the  milligrams  by  one  thousand,  to  reduce  them 
to  grams.     Record  the  complete  weight  in  the  last  column 
of  the  table. 


FUNDAMENTAL   MEASUREMENTS 


The  most  common  source  of  error  in  weighing  is  in 
summing  up  the  weights.  After  adding  the  weights  on 
the  balance,  obtain  the  sum  of  the  vacant  spaces  in  the 
block,  assigning  to  each  space  the  value  of  the  weight  it 
holds  when  it  is  in  place.  Compare  these  results. 

Conclusion.  —  Write  a  brief  statement  of  the  directions 
given  above.  This  should  be  carefully  followed  in  all  sub- 
sequent weighing.  What  is  double  weighing  ?  Look  this 
subject  up  if  you  do  not  know.  What  trouble  with  an 
imperfect  balance  does  it  overcome  ? 

EXPERIMENT  5 

Object.  —  To  study  the  curve  as  a  method  of  showing 
the  relation  between  two  quantities. 

Apparatus.  —  Millimeter  section  paper  and  a  straightedge. 
Data.  — 


CURVE  i 

CURVE  2 

CURVE  3 

SCALE  2  MM. 

SCALE  i  MM. 

SC.   I   CM.           SC.   I    MM. 

Abscissae 

Ordinates 

Abscissas 

Ordinates 

Abscissae 

Ordinates 

0 

O 

0 

10 

0 

O 

10 

10 

30 

20 

4 

4 

20 

20 

60 

30 

8 

16 

30 

30 

90 

40 

12 

36 

40 

40 

120 

50 

16 

64 

5° 

50 

150 

60 

20 

100 

60 

60 

I  80 

70 

Directions. —  About  2  cm.  from  the  edge  of  the  paper 
and   coinciding  with   one   of   the  ruled    centimeter    lines, 

PHYS.    LAB.    GUIDE 2 


8  PHYSICAL   LABORATORY    GUIDE 

draw  a  horizontal  line  lengthwise  on  a  sheet  of  section 
paper.  Mark  this  line  axis  of  X.  About  2  cm.  from  the 
left-hand  edge  of  the  paper  and  also  coinciding  with  a 
ruled  centimeter  line,  draw  a  line  at  right  angles  to  the 
axis  of  X  and  mark  this  the  axis  of  Y.  The  intersection  of 
these  axes  is  called  the  origin.  Mark  the  origin  o.  The 
origin  should  be  in  the  lower  left-hand  corner  of  the 
paper. 

Distances  measured  along  the  axis  of  X  are  called 
abscissae;  distances  measured  along  the  axis  of  Fare  called 
ordinates. 

Now  lay  off  the  distances  called  for  in  the  table  for 
curve  number  one  on  the  axes  of  Jf  and  F  Let  each  unit 
be  equal  to  2  mm.  in  this  curve.  Since  the  smallest 
values  of  both  the  abscissae  and  ordinates  are  zero,  the 
curve  begins  at  the  origin  o. 

To  locate  the  next  point  of  the  curve,  find  where  the 
vertical  line  passing  through  abscissa  10  intersects  the 
horizontal  line  passing  through  ordinate  10.  In  like  man- 
ner determine  the  other  points  of  the  curve  and  connect 
them  with  a  line. 

Plot  Curves  2  and  3  on  the  same  paper,  using  the  same 
saxes  as  in  Curve  i. 

File  these  curves  in  your  notebook  with  the  record  of 
this  experiment. 

Conclusion.  —  What  determines  the  scale  to  be  used  in 
plotting  a  curve  ?  Why  are  two  of  these  curves  straight 
lines  ?  Does  this  show  any  relation  between  the  quantities 
involved  ? 

The  third  curve  is  known  as  a  parabola.  A  projectile 
fired  horizontally  has  a  path  like  this  third  curve.  Explain 
the  advantages  of  the  Curve  in  recording  data. 


FUNDAMENTAL   MEASUREMENTS 


EXPERIMENT  6 


9 


Object.  —  To  calibrate  a  spring  balance  and  show  its 
errors-  by  a  curve. 

Apparatus.  —  A  spring  balance  (0—250  gm.),  a  set  of 
weights,  a  piece  of  thread,  millimeter  section  paper,  and  a 
30-cm.  scale. 

Data.  — 


LOAD 

BALANCE 
READING 

ERROR 

LOAD 

BALANCE 
READING 

ERROR 

Directions.  —  Attach  the  thread  to  the  balance,  using 
a  short  piece.  Its  weight  may  be  disregarded.  Note 
whether  the  balance  reads  zero  before  weights  are  attached. 
Using  a  slipknot  to  hold  the  weights,  attach  25,  50,  75  gm., 
etc.,  and  read  the  balance  each  time.  If  the  balance  reads 
more  than  the  value  of  the  weights  attached,  the  error  is 
positive ;  if  less,  negative. 

On  section  paper  draw  axes  of  X  and  Y  as  directed  in 
Experiment  5,  page  7.  On  the  axis  of  X  plot  the  loads  in 
grams  attached  to  the  balance  (scale  I  mm.  equals  I  gm.). 
On  the  axis  of  Fplot  the  corresponding  errors  (scale  I  cm. 
equals  I  gm.).  Positive  errors  should  be  plotted  above  axis 
of  X,  and  negative  values  below.  Axis  of  X  should  pass 
through  center  of  paper.  Connect  the  points  thus  deter- 
mined with  a  broken  line. 


10  PHYSICAL   LABORATORY   GUIDE 

Compare  your  curve  with  those  plotted  by  your  class- 
mates, and  decide  who  has  the  best  balance. 

Measure  the  balance  scale  with  the  metric  rule  and 
determine  whether  or  not  its  divisions  are  perfectly 
uniform. 

Conclusion. — Write  Hooke's  law.  State  whether  you 
think  the  balance  errors  are  due  to  a  failure  upon  its  part 
to  follow  Hooke's  law,  or  whether  its  failure  is  caused  by 
an  unevenly  divided  scale.  Base  your  opinion  on  your  ob- 
servations and  measurements  in  this  experiment.  Can 
you  think  of  any  other  source  of  error  ? 


CHAPTER   II 

DENSITY   AND   SPECIFIC   GRAVITY 

EXPERIMENT  7 
Object.  —  To  test  Archimedes'  principle. 

Apparatus.  —  A  balance,  a  set  of  weights,  a  solid  heavier 
than  water,  an  overflow  can,  a  catch  bucket,  a  piece  of 
thread,  and  a  jar  of  water. 

Data.  — 


OBSERVATIONS 

GRAMS 

\Veisjht  of  solid  in  air                                                    • 

\V6i°rht  of  solid  in  water 

XVcio'ht  of  empty  catch  bucket 

Weight  of  catch  bucket  and  displaced  water      .     . 
Loss  of  wei°"ht  of  solid  in  water             .          ... 

\Vei°rht  of  the  displaced  water                         ... 

Directions.  —  Suspend  the  solid  f»om  the  hook  on  the 
under  side  of  the  scalepan  of  the  balance  by  means  of  the 
piece  of  thread.  Adjust  the  length  of  the  thread  so  that 
the  solid  shall  be  in  the  center  of  the  jar  of  water  when 
the  scale  beam  is  horizontal.  Weigh  in  air  and  in  water. 
Weigh  the  empty  catch  bucket.  Cover  the  spout  of  the 
overflow  can  with  your  finger  and  fill  it  with  water.  Place 
it  on  a  level  table  and  release  your  finger,  catching  the 


12  PHYSICAL   LABORATORY  GUIDE 

surplus  water  in  the  overflow  can.  Discard  this  water. 
By  means  of  the  thread  lower  the  solid  into  the  can  and 
catch  the  displaced  water.  Weigh  this.  Calculate  the 
loss  of  weight  of  solid  in  water  and  the  weight  of  the  dis- 
placed water.  Compare  these  results. 

Conclusion.  —  State  Archimedes'  principle.  Does  your 
error  disprove  the  principle,  or  can  you  account  for  it? 
What  is  the  most  probable  source  of  error  ? 

EXPERIMENT  8 
Object.  —  To  test  the  law  of  flotation. 

Apparatus.  —  A  cylinder  weighted  to  float  upright  in 
water,  an  overflow  can,  a  catch  bucket,  a  balance,  and  a 
set  of  weights. 

Data.  — 


OBSERVATIONS 

GRAMS 

\Veijjht  of  cylinder  in  air 

Weight  of  catch  bucket  and  displaced  water  .     .     . 
Weight  of  the  displaced  water    

Error     

Directions.  —  Make  the  weighings  called  for  in  the  table. 
Follow  the  directions  given  in  Experiment  7  for  using  the 
overflow  can  and  catch  bucket.  One  end  of  the  cylinder  is 
weighted  to  make  the  block  float  upright  in  water.  When 
the  block  is  floated  in  the  overflow  can,  this  weighted  end 
should  be  immersed  first. 

Compare   the  weight  of  the   cylinder  in  air  with   the 


DENSITY   AND    SPECIFIC   GRAVITY  13 

weight  of  the  water  displaced  by  it.      What  relation  exists 
between  these  quantities  ? 

Conclusion.  —  Write  the  law  of  flotation.     Will  this  law 
hold  true  for  other  liquids  than  water  ? 


EXPERIMENT  9 
Object.  —  To  find  the  volume  of  an  irregular  solid. 

Apparatus.  —  The  irregular  body,  a  balance,  a  set  of 
weights,  a  jar  of  water,  a  loo-c.c.  graduate,  and  a  piece  of 
thread. 

Data.  — 


OBSERVATIONS 

Weight  of  body  in  air  .  ' 

\Veight  of  body  in  water                  . 

Loss  of  weight  of  body  in  water       
Volume  of  water  in  graduate  

Volume  of  water  and  body  in  graduate     .     .     .  '. 
Volume  of  the  body,  using  a  graduate       .     .     .     . 
Volume  of  the  body,  using  a  balance   

Directions.  —  Suspend  the  irregular  body  from  the  bal- 
ance as  directed  in  Experiment  5  and  weigh  it  in  air  and 
in  water.  Calculate  its  loss  of  weight  in  water.  Pour 
some  water  into  the  graduate  and  read  its  volume.  Im- 
merse the  irregular  solid  and  read  the  combined  volume  of 
solid  and  water.  Remember  to  estimate  tenths  of  the 
smallest  divisions.  Calculate  the  volume  of  the  irregular 
solid.  Compare  this  volume  with  the  loss  of  weight  of  the 
solid  in  water.  Explain  why  the  loss  of  weight  of  a  solid 


14  PHYSICAL   LABORATORY   GUIDE 

in  water  in  grams  is  equal  to  its  volume  in  cubic  centi- 
meters. Remember  that  one  cubic  centimeter  of  water 
weighs  one  gram.  Also  consult  Archimedes'  principle. 

Conclusion.  —  Which  method  is  more  likely  to  give 
accurate  results  ?  Give  your  reasons.  Could  this  method 
of  using  the  balance  for  finding  the  volume  of  a  solid  be 
used  conveniently  with  English  units  ?  Give  your  reasons. 


EXPERIMENT  10 

Object.  —  To  find  the  density  of  a  solid  that  will  sink  in 
water. 

Apparatus.  —  A  balance,  a  set  of  weights,  a  jar  of  water, 
a  piece  of  thread,  and  a  heavy  solid. 

Data.  — 


OBSERVATIONS 

Weight  of  solid  in  air    
Weight  of  solid  in  water     

Loss  of  weight  of  solid  in  water  

Volume  of  this  solid  

Density  of  this  solid       

Directions.  —  Place  the  solid  in  one  of  the  scalepans  of 
the  balance,  and  weigh.  Now  suspend  the  solid  by  the 
thread,  and  weigh  in  water.  A  correction  should  be  made 
for  the  weight  of  the  thread,  by  counterbalancing  the  thread 
with  paper  just  before  weighing  the  body  in  water,  or  better 
still  by  weighing  the  thread  and  deducting  its  weight. 

Calculate  the  loss  of  weight  in  water  and  from  this  the 
volume  of  the  solid. 


DENSITY   AND    SPECIFIC   GRAVITY  15 

Dividing  the  weight  of  the  solid  in  air  by  its  volume 
gives  the  density.  Why  ? 

Conclusion.  —  Define  density.  State  the  value  you  find 
for  the  given  substance  together  with  the  true  value  ob- 
tained from  your  instructor  or  the  tables  in  Chapter  XL 

EXPERIMENT  11 

Object.  —  To  find  the  density  of  a  solid  lighter  than 
water. 

Apparatus.  —  A  balance,  a  set  of  weights,  a  jar  of  water, 
a  sinker,  a  piece  of  thread,  and  a  piece  of  cork. 

Data.  — 


OBSERVATIONS 

\Vei°rht  of  sinker  in  water                        ..... 

\V6i°rht  of  cork  and.  sinker  in  water                  .     .     • 

Loss  of  weight  of  cork  and  sinker  in  water 
Loss  of  weight  of  sinker  alone  in  water      .... 
Loss  of  weight  of  cork  alone  in  water    

Density  of  the  cork         

Directions.  —  Make  the  four  weighings  called  for  in  the 
table,  allowing  for  the  weight  of  the  thread.  If  a  small 
loop  that  will  not  slip  is  tied  in  one  end  of  the  thread  and 
the  free  end  is  passed  through  it,  a  slipknot  which  is  readily 
untied  is  formed.  By  this  means  the  sinker  and  cork  may 
be  fastened  close  together.  Now  make  a  slipknot  in  "the 
free  end  of  the  thread.  This  affords  a  convenient  way  of 


16  PHYSICAL   LABORATORY   GUIDE 

attaching  the  sinker  and  cork  to  the  balance  and  at  the 
same  time  the  means  for  adjusting  the  height  of  the  objects 
under  water. 

Find  what  the  cork  and  sinker  together  weigh  in  air. 
Subtract  what  they  together  weigh  in  water  to  find  the 
loss  of  weight  of  both  in  water.  The  loss  of  weight  of 
sinker  alone  is  readily  found.  Knowing  how  much  weight 
both  sinker  and  cork  lose  in  water,  find  what  cork  alone 
loses  in  water.  This  will  be  the  volume  of  the  cork.  Why  ? 

Divide  the  weight  of  cork  in  air  by  its  volume  to  find  its 
density.  Why  ? 

Conclusion.  —  Define  density  and  compare  your  result 
with  the  true  density  of  cork.  Is  the  density  of  cork 
always  the  same  ?  Why  ? 

EXPERIMENT  12 

Object.  —  To  find  the  density  of  a  solid  that  is  soluble  in 
water. 

Apparatus.  —  A  balance,  a  set  of  weights,  a  jar  of  alco- 
hol, a  piece  of  copper  sulphate,  and  a  piece  of  thread. 

Data.  — 


OBSERVATIONS 

Weight  of  copper  sulphate  in  alcohol    

Density  of  alcohol  (from  table  of  densities)    . 
Loss  of  weight  in  alcohol    .               .                    .     • 

^^^eight  of  the  displaced  alcohol             .               .     • 

Volume  of  the  copper  sulphate    

Density  of  the  copper  sulphate     

DENSITY  AND   SPECIFIC   GRAVITY  17 

Directions.  —  Make  the  two  weighings  called  for  in  the 
table.  Allow  for  the  weight  of  the  thread.  Now  look  up 
the  density  of  alcohol  in  the  table  and  calculate  the  loss 
of  weight  of  copper  sulphate  in  alcohol.  What  relation 
exists  between  this  quantity  and  the  weight  of  the  displaced 
alcohol  ? 

The  density  of  alcohol  is  the  weight  of  one  cubic  centi- 
meter of  it.  Knowing  this,  how  will  you  find  the  volume 
of  the  displaced  alcohol  ?  The  volume  of  the  copper  sul- 
phate ?  The  density  of  the  copper  sulphate  ? 

Conclusion.  —  State  the  density  you  find  for  copper  sul- 
phate and  compare  it  with  the  true  value  obtained  from 
your  instructor.  Account  for  any  difference. 

EXPERIMENT  13 

Object.  —  To  find  the  density  of  a  liquid,  using  the 
density  bottle. 

Apparatus.  —  A  wide-mouthed  bottle  with  accurately  fit- 
ting glass  stopper,  a  balance,  a  set  of  weights,  and  some 
alcohol. 

Data.— 


OBSERVATIONS 

Weight  of  empty  bottle  and  stopper      .     .     .     .     . 
Weight  of  bottle  filled  with  alcohol 

Weight  of  bottle  filled  with  water     

Weight  of  alcohol  contained  in  bottle  
Weight  of  water  contained  in  bottle      
Volume  of  the  alcohol  used     

1 8  PHYSICAL  LABORATORY   GUIDE 

Directions. — Weigh  the  empty  bottle  and  be  sure  that 
it  is  clean  and  dry.  Pour  alcohol  into  the  bottle  until  the 
neck  is  half  full.  Now  put  the  stopper  firmly  in  place, 
allowing  it  to  displace  a  small  quantity  of  the  liquid.  Care 
should  be  taken  not  to  inclose  air  bubbles,  as  the  bottle 
should  be  completely  filled  with  liquid.  Make  all  observa- 
tions required  in  the  table. 

In  finding  the  volume  of  the  alcohol,  remember  that  one 
cubic  centimeter  of  water  weighs  one  gram,  and  also  that 
you  know  the  weight  of  the  water  which  the  bottle  will 
hold.  Knowing  the  weight  and  volume  of  the  alcohol  used, 
its  density  is  easily  found. 
• 

Conclusion. — State  the  density  you  find  for  alcohol  and 
compare  it  with  the  true  value.  Why  should  not  a  cork 
or  a  rubber  stopper  be  satisfactory  for  a  density  bottle? 
Knowing  the  density  of  alcohol,  what  would  its  specific 
gravity  be  ?  Why  ?  Define  specific  gravity. 

EXPERIMENT  14 

Object.  —  To  find  the  density  of  a  liquid,  using  a  Fahren- 
heit hydrometer. 

Apparatus.  —  A  Fahrenheit  hydrometer,  an  ordinary 
hydrometer  of  constant  mass,  some  alcohol,  two  hydrom- 
eter jars,  a  set  of  weights,  and  a  balance. 

Description.  —  The  Fahrenheit  hydrometer  consists  of  a 
cylindrical  shell  weighted  at  the  bottom.  This  enables  it 
to  float  upright  in  the  liquid  used.  At  the  top  is  a  long 
stem  carrying  a  scalepan  to  which  weights  may  be  added. 
A  mark  on  the  stem  indicates  the  depth  to  which  this  in- 
strument should  be  immersed. 


DENSITY   AND    SPECIFIC   GRAVITY 


Data.  — 


OBSERVATIONS 


Weight  of  Fahrenheit  hydrometer 

Additional  weight  required  to  sink  hydrometer  in 

alcohol 

Additional  weight  required  to  sink  hydrometer  in 

water 

Total   weight    (hydrometer  and   load)   floating  in 

alcohol v    . 

Total  weight  (hydrometer  and  load)  floating  in  water 

Weight  of  alcohol  displaced . 

Weight  of  water  displaced . 

Volume  of  the  alcohol . 

Density  of  the  alcohol  (Fahrenheit  hydrometer) 
Density  of  the  alcohol  (ordinary  hydrometer)    .     . 


Directions.  —  Weigh  the  Fahrenheit  hydrometer.  Place 
it  in  the  jar  of  alcohol  and  add  weights  to  its  scalepan 
until  it  just  sinks  to  the  mark  on  the  stem.  Make  the 
same  adjustment  with  the  hydrometer  floating  in  water. 
Find  the  total  weight  of  the  floating  body  in  each  case. 
What  relation  exists  between  these  values  and  the 
weights  of  alcohol  and  water  displaced  ?  Consult  Experi- 
ment 10. 

Find  the  volume  of  the  displaced  alcohol.  Note  that 
the  displaced  alcohol  and  water  have  the  same  volume. 
Why? 

Calculate  the  density  of  alcohol.  Immerse  the  hydrom- 
eter of  constant  mass  (ordinary  commercial  form)  in  the 
alcohol  and  read  its  density. 

Conclusion.  —  Compare  the  densities  found  by  the  two 
hydrometers.  Which  is  more  accurate  ?  Why  ?  Has  the 


20  PHYSICAL   LABORATORY   GUIDE 

other  any  good  qualities  ?     State  the  law  upon  which  the 
action  of  these  hydrometers  depends. 

The  terms  constant  volume  hydrometer  and  constant  mass 
hydrometer  are  sometimes  applied  to  these  instruments. 
Why  ?  What  is  the  specific  gravity  of  this  liquid  ?  Why  ? 

EXPERIMENT  15 

Object.  —  To  find  the  density  of  a  liquid  by  weighing  a 
solid  in  the  liquid  and  in  water. 

Apparatus.  —  A  large  glass  stopper  or  other  insoluble 
solid,  a  balance,  a  set  of  weights,  a  jar  of  alcohol,  a  jar  of 
water,  and  a  piece  of  thread. 

Data.  — 


OBSERVATIONS 

\Veififht  of  water  displaced  ...          

Volume  of  the  displaced  alcohol        

Density  of  the  alcohol                             .          ... 

Directions.  —  Attach  the  solid  to  the  balance  by  the 
thread  before  any  weighings  are  made.  Now  make  the 
weighings  as  shown  in  the  table.  Note  the  suggestions 
for  doing  this  in  Experiment  8.  This  will  eliminate  the 
weight  of  the  thread  from  the  final  result.  Why  ?  Find 
the  remaining  quantities  in  the  table  by  calculation  as  in 
the  preceding  experiments. 


DENSITY    AND    SPECIFIC    GRAVITY 


21 


Conclusion.  —  Compare  your  result  with 
the  true  density  of  alcohol. 

What  law  does  this  experiment  apply  ? 
What  is  the  specific  gravity  of  alcohol  ? 
Why  ?  Does  this  rule  always  hold  true  ? 

EXPERIMENT  16 

Object.  —  To  find  the  density  of  a  liquid 
by  balancing  columns. 

Apparatus.  —  Two  pieces  of  glass  tube 
about  a  meter  long,  one  piece  of  glass 
tube  about  30  cm.  long,  a  Y  tube,  rubber 
tubing  for  connecting  apparatus  as  shown 
in  Figure  I,  pinch  cock,  meter  stick,  half- 
meter  stick,  bottles  of  water  and  of  alco- 
hol. 

Data.  — 


FIG.  i. 


OBSERVATIONS 

Distance  from  table  to  alcohol  surface  in  tube     .     . 
Distance  from  table  to  alcohol  surface  in  bottle  .     . 
Length  of  effective  alcohol  column                        .     • 

Distance  from  table  to  water  surface  in  tube  . 
Distance  from  table  to  water  surface  in  bottle     .     . 
Length  of  effective  water  column  • 

Density  of  alcohol     » 

Directions.  —  Set  up  the  apparatus  as  shown  in  Figure  i. 
Partially  exhaust  the  air  from  the  apparatus  until  the  alco- 
hol is  nearly  up  to  the  top  of  the  vertical  tube.  Close  the 


22  PHYSICAL   LABORATORY   GUIDE 

pinch  cock.  Do  not  move  the  short  glass  tube,  as  this 
would  probably  change  the  heights  of  the  liquids  in  the 
tubes  slightly.  Why  ?  Be  sure  that  the  apparatus  is  per- 
fectly tight.  The  smallest  leak  would  cause  the  liquid 
columns  to  drop  slowly. 

The  effective  lengths  of  alcohol  and  water  columns  are 
the  distances  from  the  surfaces  of  the  liquids  in  the  bottles 
to  the  surfaces  of  the  liquids  in  the  tubes.  It  is  difficult  to 
measure  these  lengths  directly.  It  is  better  to  calculate 
their  values  from  the  measurements  called  for  in  the  table. 
Dividing  the  effective  length  of  water  column  by  the  effec- 
tive length  of  alcohol  column  gives  the  density  of  alcohol, 
for  these  columns  are  of  equal  weight.  Why  ?  Also 
their  volumes  are  proportional  to  their  lengths.  Therefore, 
remembering  that  the  density  of  water  is  one  gram,  we 
can  make  an  inverse  proposition  between  the  two  densities 
and  the  two  column  lengths,  or,  which  amounts  to  the 
same  thing,  divide  the  water  by  the  alcohol  column  as 
given  above. 

Conclusion.  —  Compare  all  the  methods  you  have  used 
for  finding  the  density  of  a  liquid.  Which  is  most  accu- 
rate ?  Which  is  of  greatest  value  commercially  ? 


CHAPTER   III 

MAGNETISM 
EXPERIMENT  17 

Object.  —  To  plot  the  field  about  a  bar  magnet  by  means 
of  a  small  compass. 

Apparatus.  —  A  sheet  of  paper  30  x  50  cm.,  a  bar  mag- 
net, and  a  compass. 

Directions.  —  Place  the  sheet  of  paper  upon  the  table 
with  the  magnet  in  the  center  of  the  paper,  the  north-seek- 
ing end  of  the  magnet  pointing  north.  Draw  the  outline 
of  the  magnet.  (It  is  possible  to  find  the  magnetic  merid- 
ian and  also  to  determine  the  north-seeking  end  of  the 
bar  magnet  with  the  apparatus  given.  How  ?)  Now 
place  the  compass  near  one  corner  of  the  magnet.  With 
your  pencil  place  a  dot  on  the  paper  to  show  the  position 
of  the  end  of  the  needle  farthest  from  the  magnet.  Move 
the  compass  until  the  end  of  the  needle  nearest  the  mag- 
net coincides  with  the  dpt.  Indicate  the  new  position  of 
the  other  end  by  a  second  dot.  Proceed  in  this  way  until 
you  reach  the  other  pole  of  the  magnet  or  the  edge  of  the 
paper.  Carefully  draw  a  curved  line  through  the  dots,  in- 
dicating the  direction  in  which  the  north-seeking  end  of 
the  compass  points  along  this  line  by  an  arrow.  In  the 
same  manner  draw  other  lines,  starting  from  different 
points  on  the  sides  and  ends  of  the  magnet. 

PHYS.  LAB.  GUIDE — 3  23 


24  PHYSICAL   LABORATORY   GUIDE 

When  you  have  drawn  a  sufficient  number  of  lines  to 
show  the  direction  of  the  field  on  all  parts  of  the  paper, 
place  the  compass  on  the  bar  magnet  and  move  it  back 
and  forth,  noting  the  direction  in  which  the  needle  points. 
What  does  this  indicate  regarding  the  direction  of  the 
magnetic  force  within  the  magnet  ?  Using  dotted  lines  to 
show  the  direction  of  the  magnetic  force  within  the  mag- 
net, complete  the  drawing.  Mark  the  poles  of  the  mag- 
net N  and  S. 

Fold  the  completed  drawing  to  a  convenient  size  and 
file  in  your  notebook. 

Conclusion.  —  Where  do  the  lines  of  force  begin  and 
end  ?  Do  any  two  lines  intersect  ?  What  is  the  direction 
of  the  magnetic  force  within  the  magnet  ?  Why  do  the 
lines  drawn  represent  the  direction  of  magnetic  force  in 
the  field  about  the  bar  magnet  ? 

EXPERIMENT  18 

Object.  —  To  plot  several  magnetic  fields  by  means  of 
iron  filings. 

Apparatus.  —  Two  bar  magnets,  iron  filings,  a  wire- 
gauze  sieve,  thumb  tacks,  blue-print  paper  (6"  X  8"),  a 
large  jar  of  water,  a  board  8"  x  14"  with  slot  i"  wide  and 
\"  deep  running  lengthwise  through  the  center,  to  hold 
magnets. 

Directions.  —  Place  one  of  the  magnets  in  the  slot  of 
the  board  and  cover  it  with  a  sheet  of  blue-print  paper, 
placing  the  sensitive  side  up.  Be  careful  to  have  the  mag- 
net in  the  center  of  the  paper.  Fasten  the  paper  in  posi- 
tion with  thumb  tacks.  Write  your  name  in  a  corner  of 


MAGNETISM  25 

the  paper.  Now  sprinkle  filings  evenly  over  the  paper, 
holding  the  sieve  about  a  foot  above  it  and  tapping  the 
sieve  gently  to  release  the  filings.  Avoid  using  too  many. 
A  light  covering  will  show  the  details  of  the  field  best. 
Now  expose  the  apparatus  as  arranged  to  direct  sunlight 
for  five  minutes.  Then  remove  the  filings  and  immerse 
the  blue  print  in  water,  washing  it  thoroughly.  Place  the 
print  face  down  on  a  clean  pane  of  glass  to  dry.  Then 
file  it  in  your  notebook. 

Make  prints  also  :  (a)  of  the  field  about  two  unlike  poles ; 
(b)  about  two  like  poles.  Use  separate  magnets  with  the 
poles  about  3  cm.  apart. 

Conclusion.  —  State  what  each  print  shows  as  to  the 
direction  and  arrangement  of  the  magnetic  field.  Why  do 
the  filings  show  the  directions  of  the  lines  of  force  ?  State 
the  principle  involved. 

NOTE.  —  If  sunlight  is  not  available,  excellent  results  may  be 
obtained  by  using  an  arc  light  and  placing  the  paper  to  be  printed  not 
more  than  i|  feet  away  from  the  arc  and  under  it.  The  time  required 
under  these  conditions  will  not  exceed  ten  minutes  with  a  2o-ampere 
arc.  Unless  the  sun^  rays  are  nearly  vertical,  the  filings  will  cast 
shadows  which  are  very  different  in  size  and  shape  from  the  filings 
themselves.  This  is  a  serious  objection,  and  the  arc-light,  although 
slower,  is  much  to  be  preferred. 

EXPERIMENT  19 

Object.  —  To  investigate  the  magnetic  field  surrounding 
a  single  conductor  carrying  an  electric  current. 

Apparatus.  —  About  a  meter  of  insulated  copper  wire 
(20  B.  &  S.  gauge),  some  source  of  direct  current  (about 
2  or  3  amperes),  a  small  magnetic  compass  with  graduated 
scale,  a  small  wooden  block,  and  a  ruler. 


6                      PHYSICAL    LABORATORY   GUIDE 

Data.  — 

POSITION  OF 
WIRE 

DIRECTION  OF 
CURRENT 

DIRECTION  OF 
DEFLECTION 

MAGNITUDE  OF 
DEFLECTION 

Directions.  —  Draw  two  perpendicular  lines  about  10 
cm.  long  each  and  intersecting  in  the  center  of  your 
notebook  page.  Place  your  compass  so  that  its  center 
and  the  intersection  of  the  lines  just  drawn  coincide. 
Trace  the  outline  of  the  compass.  Using  the  letters  N, 
S,  etc.,  etc.,  indicate  the  points  of  the  compass  on  the  ends 
of  the  intersecting  lines.  These  should  give  the  true 
directions  of  the  four  chief  points  of  the  compass  when 
the  notebook  is  before  you  in  the  usual  convenient  position 
for  use. 

Place  compass  in  the  circle  and  have  the  north  and  south 
lines  of  the  diagram  and  the  compass  scale  coincide  with 
the  direction  of  the  magnetic  needle.  All  three  will  now 
be  in  the  magnetic  meridian.  Place  the  conductor  parallel 
to  the  north  and  south  line  of  the  diagram,  with  the  current 
flowing  from  south  to  north.  Note  the  direction  and  mag- 
nitude of  the  deflection  and  record  in  the  table.  Reverse 
the  current  and  again  test  and  record.  In  like  manner, 
test  with  the  conductor  below  the  needle.  Reverse  the 
current  and  test  again.  Now  place  the  conductor  along 
the  east  and  west  line  both  above  and  below  the  needle, 
and  in  both  cases  try  the  current  first  in  one  direction  and 
then  in  the  other.  Record  all  results. 


MAGNETISM  27 

Place  the  compass  on  the  block  and  hold  the  wire  in  a 
vertical  position  near  the  compass  and  on  its  north  side. 
Test  with  the  current  in  both  directions.  Also  hold  the 
wire  just  south  of  the  compass  and  try  the  deflection  with 
current  flowing  up  and  then  down  through  the  wire.  You 
will  now  have  made  twelve  different  tests. 

Conclusion.  —  State  the  relative  position  of  the  conductor 
and  the  lines  of  force  as  shown  by  this  experiment. 

Test  the  following  rules  by  applying  them  to  the  results 
you  have  just  obtained;  then  include  them  in  your  con- 
clusion : 

1.  Place  the  right  hand  in  such  a  position  that  the  palm 
faces  the  compass  and  the  conductor  is  between  the  com- 
pass and   your  hand.     Then   if   the  outstretched   fingers 
point  in  the  direction  in  which  the  current  is  flowing,  the 
extended  thumb  will  show  the  direction  in  which  the  north- 
seeking  end  of  the  needle  will  deflect. 

2.  If  an  ordinary  right-handed,  wood  screw  is  turned 
by  means  of  a  screw  driver,  and  if  its  forward  motion  into 
the  wood  is  made  to  represent  the  direction  in  which  a 
current  is  flowing  along  a  conductor,  then  the  direction 
of  circular  motion  of  the  handle  of  the  screw  driver  will 
show  the  direction  of  the  lines  of  magnetic  force  surround- 
ing it. 

3.  Looking   at  the  end   of   a   conductor  in   which    an 
electric  current  is  flowing,  state  whether  the  lines  of  force 
are  clockwise  or  counterclockwise  when  the  current  flows 
toward  you,  and  vice  versa. 

NOTE.  —  The  pupil  should  make  a  special  effort  to  gain  a  very  clear 
idea  of  the  relative  positions  of  the  current  and  the  lines  of  magnetic 
force  from  this  experiment.  The  rules  just  given  are  secondary  to 
this. 


28 


PHYSICAL   LABORATORY   GUIDE 


EXPERIMENT  20 

Object.  —  To  map  out  the  lines  of  magnetic  force  about 
a  galvanoscope. 

Apparatus.  —  A  galvanoscope,  a  compass,  a  ruler,  and  a 
source  of  direct  current. 

Directions.  —  Draw  a  diagram  in  your  notebook  like  the 
one  shown  in  Figure  2.  This  will  represent  roughly  a 
section  of  the  galvanoscope  as  it  would  appear  if  seen  from 


FIG.  2. 

above  with  the  upper  half  of  the  coil  removed.  The  small 
circles  show  the  wires  of  the  coil.  Use  a  plus  sign  to 
mark  those  wires  in  which  the  current  is  flowing  toward 
you.  Use  a  minus  sign  to  indicate  those  wires  in  which 
the  current  is  flowing  away  from  you.  Now  place  the  gal- 
vanoscope so  that  its  coil  is  in  the  magnetic  meridian,  and 
pass  a  current  of  about  five  amperes  through  it  in  the 
direction  indicated.  Hold  the  compass  in  position  a  and 
draw  an  arrow  to  indicate  the  direction  in  which  the  north- 
seeking  end  of  the  needle  points. 

In  like  manner  test  the  direction  of  the  magnetic  field  at 
points  b,  c,  d  and  a',  b',  c{ ',  and  </,  recording  the  results  with 
arrows  on  your  drawing  as  before. 


MAGNETISM  29 

Next,  reverse  the  current  through  the  galvanoscope  and 
again  test  the  direction  of  the  magnetic  field.  Record  the 
results  you  obtain  by  means  of  arrows,  using  a  second 
diagram. 

Now  place  the  compass  in  its  normal  position  on  the 
crossbar  of  the  galvanoscope  and  draw  an  arrow  in  the 
center  of  the  diagram  to  show  the  direction  in  which  it 
points.  Reverse  the  current  and  again  show  the  deflection 
of  the  needle  on  the  first  diagram. 

Conclusion. — Why  is  the  needle  of  a  galvanoscope  de- 
flected when  a  current  passes  through  its  coil  ?  Why  does 
reversing  the  current  reverse  the  direction  in  which  the 
needle  deflects  ?  The  circuit  carrying  the  electric  current 
is  a  closed  loop.  Are  the  magnetic  lines  of  force  also 
closed  loops  ?  What  is  the  direction  of  these  loops  relative 
to  the  coil  ? 


CHAPTER  IV 

VOLTAIC  CELLS  AND  THERMOCURRENTS 

EXPERIMENT  21 
Object.  —  To  study  the  action  of  a  simple  voltaic  cell. 

Apparatus.  —  Materials  for  a  small  copper-zinc  cell; 
(see  description  of  cell  in  Chap.  XII),  dilute  sulphuric 
acid  (about  twenty  parts  by  volume  of  water  to  one  part 
of  concentrated  acid),  a  galvanoscope  and  connecting 
wires,  two  zinc  plates  (one  amalgamated),  and  emery 
cloth. 

Data.  — 


OBSERVATIONS 

DEFLECTION 

The  galvanoscope  was  read  at  one-minute 
intervals  for  five  minutes. 

Directions.  —  Scour  the  copper  plate  with  the  emery  cloth 
until  as  much  of  the  plate  as  will  be  immersed  in  the  acid 
is  clean  and  bright.  Fasten  the  unamalgamated  zinc  and 
copper  plates  to  the  wooden  crossbar  and  immerse  them 
in  the  acid.  Observe  carefully  any  action  on  the  surfaces 
of  the  plates.  The  circuit  should  be  open  for  this  test. 

Now  close  the  circuit  of  the  battery  by  means  of  a  cop- 
per wire  connected  to  the  zinc  and  copper  plates  and 

30 


VOLTAIC   CELLS   AND   THERMOCURRENTS  31 

again  observe  carefully  any  action  taking  place  on  the 
surfaces  of  the  plates.  Record  these  results. 

Next  remove  the  zinc  plate  and  put  the  amalgamated 
zinc  in  its  place.  Leaving  the  circuit  open  again,  note 
any  action  upon  the  plates  when  they  are  immersed 
in  the  acid.  Compare  the  result  in  this  case  with  the 
result  you  obtained  under  the  same  conditions  with 
the  unamalgamated  zinc.  Account  for  the  differ- 
ence. What  is  the  action  on  the  unamalgamated  zinc 
called  ?  Why  does  amalgamating  the  zinc  overcome  this 
difficulty  ? 

Place  the  galvanoscope  so  that  the  coil  of  wire  and  the 
compass  scale  are  in  the  magnetic  meridian.  Close  the 
circuit  of  the  battery  through  the  fifteen  turns  of  the  gal- 
vanoscope and  read  the  deflection  of  the  magnetic  needle 
at  intervals  of  one  minute  for  five  minutes.  The  cell 
should  not  be  shaken  or  disturbed  in  any  way  during  this 
time.  If  no  decided  change  occurs  in  the  deflection,  re- 
move the  copper  plate,  rinse  it,  and  again  scour  it  with 
emery  cloth.  Put  the  cell  together,  using  a  fresh  supply 
of  acid.  Again  take  readings  at  one-minute  intervals. 
Record  the  readings  in  the  table.  Account  for  the  change 
in  the  deflection.  What  is  this  phenomenon  called?  Ex- 
plain its  cause  fully.  Draw  a  diagram  of  this  cell  in  your 
notebook,  marking  the  plates  and  solution. 

Conclusion.  —  What  is  the  gas  which  is  disengaged  dur- 
ing the  operation  of  the  battery?  Write  the  chemical  ac- 
tion which  takes  place.  What  are  the  weak  points  of  a 
simple  voltaic  cell  of  this  kind?  Give  their  technical 
names.  How  did  you  correct  one  of  these  difficulties  in 
this  experiment  ?  The  next  experiment  will  suggest  a 
remedy  for  the  other. 


32  PHYSICAL   LABORATORY   GUIDE 

EXPERIMENT  22 
Object.  — To  study  a  Daniell  cell.     (Method  i.) 

Apparatus.  —  A  small  Daniell  cell,  dilute  sulphuric  acid 
and  solution  of  copper  sulphate,  a  galvanoscope  and  con- 
necting wires.  The  zinc  should  be  well  amalgamated. 

Data.  — 


OBSERVATIONS 

SIMPLE  CELL 

DANIELL  CELL 

The  galvanoscope  was  read  at  one- 
minute  intervals  for  five  minutes. 

Directions.  —  Set  up  the  cell  ready  for  use.  Close  the 
circuit  with  a  short  piece  of  copper  wire.  The  Daniell 
cell  is  a  closed  circuit  battery  and  should  not  be  left  for  any 
period  of  time  on  open  circuit.  Why  not  ?  Draw  a  dia- 
gram of  the  cell  in  your  notebook,  marking  the  plates  and 
solutions.  Examine  the  cell  carefully  for  any  evidence  of 
action.  Now  remove  the  copper  plate  part  way  from  the 
copper  sulphate  solution  and  note  the  appearance  of  its 
surface.  Replace  it  in  position. 

Set  up  the  galvanoscope  in  the  usual  manner,  connect- 
ing the  Daniell  cell  with  the  coil  of  fifteen  turns.  Take 
readings  every  minute  for  five  minutes  and  record  the  de- 
flections in  the  table.  Copy  the  readings  taken  with  the 
simple  cell  in  the  last  experiment  and  compare  the 
results.  Explain  the  chemistry  of  the  Daniell  cell  as 
fully  as  you  can. 

Conclusion.  —  Hydrogen  is  not  disengaged  by  this  cell. 
Why  not  ?  Why  does  the  copper  plate  become  brighter 


VOLTAIC   CELLS   AND   THERMOCURRENTS  33 

after  the  action  of  the  cell  has  continued  for  a  time  ?  How 
are  local  action  and  polarization  overcome  in  this  type  of 
cell  ?  For  what  kind  of  work  is  the  Daniell  cell  suited  ? 
Why  would  it  not  be  satisfactory  for  operating  doorbells  ? 

EXPERIMENT  22   (Continued-) 
Object.  —  To  study  the  Daniell  cell.     (Method  2.) 

Apparatus.  —  A  Daniell  cell,  dilute  sulphuric  acid,  copper 
sulphate  solution,  an  ammeter,  connecting  wires,  a  balance, 
and  a  set  of  weights. 

Data.— 


OBSERVATIONS 

Weight,  of  copper  plate  before  closing  circuit      .     . 
Weight  of  copper  plate  after  15  minutes    .     .     .     . 
Weight  of  copper  deposited  in  15  minutes      .     .    V 
Weight  of  copper  deposited  by  i  amp.  in  15  minutes 
(cal.)  . 

Directions.  —  Set  up  the  cell  ready  for  use.  Close  the 
circuit  at  once  with  a  short  piece  of  copper  wire.  The 
Daniell  cell  is  a  closed  circuit  battery  and  should  not  be 
left  for  any  period  of  time  on  open  circuit.  Why  not? 
Draw  a  diagram  of  the  cell  in  your  notebook,  marking  the 
plates  and  solutions.  Examine  the  cell  carefully  for  any 
evidence  of  action,  noting  the  appearance  of  the  immersed 
surface  of  the  copper  plate. 

Now  remove  the  copper  plate  from  the  cell.  After 
washing  and  drying  it,  place  it  on  the  balance  and  weigh. 


34  PHYSICAL   LABORATORY   GUIDE 

Put  the  cell  together  again  and  close  the  circuit  through 
the  ammeter.  Allow  the  current  to  flow  for  fifteen  min- 
utes. The  timing  must  be  accurately  done.  Read  the 
ammeter.  Again  remove  the  copper  plate,  wash,  dry,  and 
weigh  it. 

From  the  electrochemical  equivalent  of  copper  (weight 
of  copper  deposited  by  one  ampere  in  one  second),  found 
in  the  tables,  calculate  how  much  copper  one  ampere  would 
deposit  in  fifteen  minutes.  By  comparing  this  value  with 
the  weight  of  copper  deposited  by  the  Daniell  cell,  find 
the  strength  of  its  current.  Compare  this  with  the  reading 
of  the  ammeter. 

Conclusion.  —  Was  hydrogen  disengaged  by  the  cell  ? 
Why  does  the  copper  plate  become  brighter  after  the 
action  of  this  cell  has  continued  for  some  time  ?  How 
are  local  action  and  polarization  overcome  in  this  type  of 
cell  ?  Describe  the  chemistry  of  this  cell.  For  what  kind 
of  work  is  the  Daniell  cell  suited  ?  Why  would  it  be 
unsatisfactory  for  operating  doorbells  ? 


EXPERIMENT  23 

Object.  —  To  study  the  thermoelectric  current  produced 
where  a  junction  of  iron  and  copper  wire  is  heated. 

Apparatus.  —  A  galvanometer,  a  Bun  sen  burner,  two 
pieces  of  copper  wire  about  30  cm.  long,  a  piece  of  iron 
wire  about  30  cm.  long,  a  voltaic  cell,  and  a  resistance  box. 

NOTE.  —  Thermocurrents  are  applied  practically  in  instruments 
called  pyrometers.  The  contact  of  two  unlike  metals  is  placed  in  the 
source  of  a  high  temperature,  such  as  molten  iron,  and  the  temperature 
estimated  from  the  galvanometer  reading. 


VOLTAIC   CELLS    AND   THERMOCURRENTS 

Data.  — 


35 


OBSERVATIONS 

DEFLECTIONS 

Direction 

Degrees 

Junction  (i)  heated  with  the  hand  . 
Junction  (2)  heated  with  the  hand   . 
Junction    (i)    heated    gently  above 
burner 

Junction    (2)    heated    gently   above 
burner      

Junction    (i)    heated     strongly     in 
burner      .               

Junction    (2)    heated     strongly     in 
burner 

Directions.  —  Connect  apparatus  as  shown  in  Fig.  3, 
twisting  the  copper  and  iron  wires  together  to  form  junc- 
tions number  (i)  and  (2). 

Heat  (i)  and  (2)  in  succession  by  holding  between  the 
thumb  and  finger.  Sufficient  time  must  be  given  for  the 
first  junction  to  cool  before  heating  the  second. 

Now  heat  the  junctions  by  holding  them  in  succession 
just  above  the  Bunsen  flame.  Remove  oxide  from  junc- 
tions by  scraping.  Wires  at  cool  junction  should  make 
good  contact. 

Next,  heat  them  to  a  red  heat  in  the  flame.  Allow 
one  junction  to  cool  in  every  case  before  heating  the 
second. 

Record  both  the  directions  and  the  magnitudes  of  the  de- 
flections. 

Place  the  battery  and  resistance  box  in  series  with  the 
galvanometer,  and  note  the  relation  between  the  direction 
of  the  current  and  the  direction  of  the  deflections. 


PHYSICAL   LABORATORY   GUIDE 


Fe 
FIG.  3. 

Conclusion.  —  Upon  what  does  the  strength  of  the  thermo 
current  depend  ?  Does  the  current  flow  from  the  copper 
to  the  iron,  or  vice  versa  ?  Is  this  rule  true  for  all  tem- 
peratures ?  Is  there  any  temperature  at  which  the  thermo- 
current  is  zero  ?  If  both  junctions  were  heated  equally  at 
the  same  time,  would  the  galvanometer  show  any  deflec- 
tion ?  Try  it. 


CHAPTER   V 

ELECTRICAL  TESTING 
EXPERIMENT  24.    PART  1 

Object.  —  To  find  how  the  deflection  of  a  galvanometer 
varies  with  the  resistance  in  circuit. 

Apparatus.  —  An  astatic  galvanometer,  a  resistance  box, 
a  reversing  switch,  a  small  Daniell  cell,  connecting  wires, 
and  an  adjustable  shunt.  (See  Appendix.) 

Data.  — 


OHMS  IN  Box 

DEFLECTION 
RIGHT 

DEFLECTION 
LEFT 

DEFLECTION 
AVERAGE 

Directions.  —  Level  and  adjust  the  galvanometer  until 
the  pointer  stands  at  zero.  Connect  the  apparatus  as 
shown  in  Figure  4.  The  switch  must  be  left  open  until 
all  connections  have  been  made.  All  contacts  should  be 
bright  and  firm.  Put  100  ohms  in  the  box  by  removing 
the  required  number  of  plugs,  and  close  the  switch.  Only 
a  momentary  contact  should  be  made.  When  the  needle 

37 


PHYSICAL   LABORATORY   GUIDE 


reaches  the  limit  of  its  swing,  close  the  switch  momentarily 
again.  In  doing  this,  cause  the  needle  to  advance  about 
10°  with  each  contact  until  no  further  increase  in  the  de- 
flection takes  place,  then  close  the  switch. 

Practice  this  method  of  bringing  the  galvanometer  to  its 
deflection  until  you  are  able  to  bring  the  needle  to  rest 


FIG.  4. 

with  practically  no  oscillations.  When  the  circuit  is  to  be 
broken,  the  needle  can  be  brought  to  rest  very  quickly  by 
checking  its  backward  motion  from  time  to  time  by  closing 
the  circuit  for  an  instant. 

Shifting  the  contact  piece  through  a  right  angle  reverses 
the  deflection  of  the  galvanometer ;  try  it.  Trace  out  the 
connections  until  you  see  why  this  is  so. 

Now  connect  the  shunt  to  the  galvanometer,  using  a 
loop  of  copper  wire  with  the  ends  dipping  into  the  mercury 
cups.  Note  that  now  only  a  part  of  the  current  passes 


ELECTRICAL   TESTING  39 

through  the  galvanometer,  the  balance  going  through  the 
shunt. 

Shorten  the  shunt  by  twisting  the  looped  end  together. 
This  will  lower  its  resistance,  causing  it  to  take  more  of 
the  current  and  consequently  decreasing  the  galvanometer 
deflection.  Continue  adjusting  the  shunt  until  with  100 
ohms  in  the  box  the  deflection  of  the  galvanometer  is 
approximately  30°.  Read  the  deflection  accurately.  Re- 
verse the  current  and  read  the  deflection  in  the  opposite 
direction.  Change  the  resistance  in  the  box  to  90  ohms 
and  again  read  the  right  and  left  deflections.  Continue  in 
this  manner,  decreasing  the  resistance  10  ohms  at  a  time, 
reading  the  deflections  until  they  are  more  than  80°. 
Record  the  results  in  the  table. 

Conclusion.  —  Are  the  right  and  left  deflections  equal  ? 
Can  you  account  for  this?.  Would  a  failure  upon  the  part 
of  a  galvanometer  to  return  perfectly  to  zero,  after  each 
deflection,  seriously  affect  the  average  deflection  ?  Is  there 
any  simple  relation  between  the  resistance  in  circuit  and 
the  deflection  produced  with  an  astatic  galvanometer  ? 

NOTE.  —  As  the  reversing  key,  galvanometer,  and  resistance  box  will 
be  used  in  a  number  of  subsequent  experiments,  the  pupil  should  now 
become  as  familiar  as  possible  with  their  manipulation. 


EXPERIMENT  24.     PART   2 

Object.  —  To  show  the  relation  between  the  resistance 
in  circuit  and  the  deflection  of  a  galvanometer  by  means  of 
a  curve. 

Apparatus.  —  Millimeter  section  paper,  a  ruler,  and  the 
data  from  Part  i. 

PHYS.  LAB.  GUIDE  —  4 


40  PHYSICAL   LABORATORY   GUIDE 

Directions.  —  Following  the  directions  given  in  Experi- 
ment 5,  draw  the  axes  of  X  and  Y.  Using  a  convenient 
scale,  plot  the  values  of  the  resistances  in  circuit  as  the 
abscissae  along  the  axis  of  X,  and  make  the  values  of 
the  deflections  the  ordinates  along  the  axis  of  Y.  Find  the 
intersections,  in  each  case,  of  perpendiculars  through  corre- 
sponding points  just  plotted,  on  X  and  Y.  Through  the 
intersections  draw  the  curve.  The  data  taken  in  Part  I 
should  be  used  for  this  curve.  Using  a  tangent  instead 
of  the  astatic  galvanometer,  take  readings  similar  to  those 
in  Part  I.  It  will  probably  not  be  necessary  to  use  the 
shunt  in  this  case.  Plot  these  results  on  the  same  paper 
with  the  curve  for  the  astatic  galvanometer.  Mark  each 
curve. 

Conclusion.  —  Compare  the  curves  just  drawn.  From 
the  character  of  these  curves,  what  resistance  would  you 
say  would  be  necessary  to  make  the  galvanometer  read 
zero  ?  Does  the  resistance  of  an  open  circuit  approximate 
this  value  ? 

EXPERIMENT  25 

Object.  —  To  measure  the  resistance  of  several  conduc- 
tors by  the  method  of  substitution. 

Apparatus.  —  Astatic  galvanometer,  resistance  box,  re- 
versing switch,  Daniell  cell,  connecting  wires,  and  several 
unknown  resistances. 

NOTE.  —  While  other  forms  of  galvanometer  may  be  used  in  this 
and  the  following  experiments,  the  astatic  form  is  the  simplest.  The 
movable  part  consists  of  two  magnets  of  equal  size  and  strength  rigidly 
fastened  with  their  like  poles  pointing  in  opposite  directions.  See  de- 
scription Chapter  XI. 


ELECTRICAL   TESTING 


Data.  — 


OBSERVATIONS 

i 

2 

3 

Deflection  to  the  right  .... 
Deflection  to  the  left     .     .     .     .'  | 
Average  deflection    
Ohms  in  box  with  x  in  circuit 
Ohms  in  box  with  x  cut  out  .     . 
Resistance  of  conductor  x      .     . 

Directions.  —  Connect  the  apparatus  as  shown  in  Fig- 
ure   5.     Level   and   adjust   galvanometer   to    zero.      Put 


FIG.  5. 

50  ohms  in  the  box  and  try  the  galvanometer  deflection. 
It  should  be  between  20°  and  80°.  If  the  deflection 
is  too  high,  adjust  a  shunt  to  the  galvanometer.  The 


42  PHYSICAL   LABORATORY   GUIDE 

remedy  for  too  low  a  reading  is  obvious.  Read  the  right 
and  left  deflections  and  calculate  the  average. 

Bring  the  galvanometer  to  zero  and  then  remove  the 
resistance  x  from  the  circuit,  putting  in  its  place  a  copper 
wire  whose  resistance  is  very  low.  Now  increase  the  re- 
sistance in  the  box  until  the  deflection  to  the  right  is  the 
same  as  before.  Try  the  deflection  to  the  left ;  it  should 
also  be  the  same.  If  it  is  not,  the  zero  reading  of  the 
galvanometer  has  changed,  in  which  case  adjust  the 
resistance  in  the  box  until  a  right  and  a  left  deflection 
is  obtained,  which  will  give  the  same  average  deflec- 
tion as  was  found  when  the  unknown  resistance  was  in 
circuit. 

From  this  data  calculate  the  value  of  x.  Remember 
that  the  e.  m.  f.  and  current  are  the  same  in  both  cases. 
What  about  the  value  of  the  total  resistance  ?  Of  what 
does  the  increase  in  the  resistance  in  the  box  take  the 
place  ?  In  like  manner  measure  other  resistances. 

Conclusion.  —  Would  this  method  work  with  a  battery  of 
variable  e.  m.  f .  ?  Why?  Would  this  be  a  good  method 
for  measuring  resistances  where  their  values  covered  a 
very  great  range  ?  Give  reasons  for  your  answer. 


EXPERIMENT  26 

Object.  —  To  compare  the  e.  m.  f.  of  a  dry  cell  with  the 
e.  m.  f.  of  a  Daniell  cell  by  the  equal  deflection  method. 

Apparatus.  —  A  galvanometer,  a  resistance  box,  a  revers- 
ing key,  a  dry  cell,  a  Daniell  cell,  and  connecting  wires. 

(Diagram  of  connections  is  like  Figure  4.) 


ELECTRICAL   TESTING 


43 


Data.  — 


OBSERVATIONS 

SYMBOL 

VALUE 

Deflection  of  galvanometer    .... 
Resistance  in  box  —  dry  cell  .... 
Resistance  in  box  —  Daniell  cell      .     . 
E.  M.  F.  of  Daniell  cell  (known)     .     . 
E.  M.  F.  of  dry  cell  (calculated)      . 

Ri 

fa 

Si 

£2 

Directions.  —  Connect  the  apparatus  as  shown  in  the 
diagram,  putting  the  dry  cell  in  circuit  first.  Place  the 
necessary  resistance  in  the  box  to  give  some  convenient 
deflection.  It  is  desirable  that  this  resistance  be  as  high 
as  practicable,  but  the  deflection  should  not  be  less  than 
25.  Now  place  the  Daniell  cell  in  circuit  instead  of  the 
dry  cell.  Adjust  the  resistance  in  the  box  until  the  deflec- 
tion is  the  same  as  before,  both  in  direction  and  magnitude. 

Caution.  — The  zero  reading  of  the  galvanometer  should 
be  observed  after  each  deflection.  If  the  galvanometer 
does  not  return  perfectly  to  the  same  zero  each  time,  then 
each  reading  made  above  should  be  the  average  of  an  east 
and  a  west  deflection. 

Applying  Ohm's  law  and  remembering  that  with  the 
same  galvanometer  equal  deflections  mean  equal  currents, 
we  have : 


Conclusion.  —  Why  is  it  desirable  to  have  a  considerable 
resistance  in  the  box  for  this  experiment?  Would  it  be 
possible  to  obtain  accurate  results  with  a  low  resistance  in 
the  box  ?  Give  a  reason  for  your  answer. 


44 


PHYSICAL   LABORATORY   GUIDE 


EXPERIMENT  27 


Object.  —  To  measure  several  resistances  with  a  Wheat- 
stone  bridge. 

Apparatus.  —  A  Wheatstone  bridge,  a  galvanometer,  a 
dry  cell,  several  resistances,  and  connecting  wires.  (See 
Appendix  for  special  form  of  Wheatstone  bridge.) 

Data.  — 


OBJECT  MEASURED 

RATIO 

OHMS  IN  Box 

VALUE  OF  x 

Directions.  —  Connect  the  apparatus  as  shown  in  Fig- 
ure 6.  Compare  the  connections  with  the  theoretical 
diagram  of  the  Wheatstone  bridge  shown  in  Figure  7  on 
page  46. 

Now  short-circuit  the  one-ohm  coils,  leaving  the  ratio  \§. 
Take  a  very  small  resistance  out  of  the  box,  one  that  you 
are  quite  certain  is  smaller  than  the  value  of  x.  Depress 
the  battery  key  Ba.  Hold  this  down  and  then  depress  the 
galvanometer  key  Ga  for  just  an  instant.  Note  the  direc- 
tion in  which  the  galvanometer  deflects.  Next  put  a  resist- 
ance in  the  box  which  is  larger  than  x.  Again  press  down 
first  Ba  an-d  then  Ga.  The  galvanometer  should  now 


ELECTRICAL   TESTING 


45 


deflect  in  the  opposite  direction.     Make  a  note  of  these 
directions. 

Now  place  a  resistance  in  the  box  which  you  think  is  near 
the  value  of  x.  Find  out  whether  it  is  too  large  or  too  small 
by  testing  the  deflection  of  the  galvanometer.  Keep  on 
adjusting  the  resistance  until  depressing  the  keys  does  not 


i—/-  1 

(f¥o 

O  O  O 

o  o 

fcj)  Q 

o  o  o 

o  o 

j£* 

FIG.  6. 

deflect  the  galvanometer.  Care  should  be  taken  always  to 
close  the  battery  key  first.  While  holding  it  down,  close 
the  galvanometer  key.  If  this  precaution  is  not  taken,  the 
galvanometer  will  show  a  deflection  due  to  induction  in  the 
circuit  even  when  the  bridge  is  correctly  balanced. 
When  the  bridge  is  balanced : 


r<i\rn  = 


or  x  =      - 


Substituting  in  equation  (i),  the  value  of  x  is  readily  found. 
Measure  several  resistances  in  the  same  manner. 


46  PHYSICAL   LABORATORY   GUIDE 

The  values  of  the  resistances  in  the  box  may  be  multi- 
plied or  divided  by  10  by  using  ratios  1-f-  or  ^  instead  of 
\  or  if 


FIG.  7. 

Conclusion.  •—  Compare  the  Wheatstone  bridge  method  of 
measuring  resistance  with  the  method  of  substitution.  State 
the  advantages  of  the  bridge  method. 


ELECTRICAL   TESTING 


47 


EXPERIMENT  28 

Object.  —  To  measure  the  internal  resistance  of  a  cell  of 
battery  by  the  method  of  opposition. 

Apparatus.  —  A  Wheatstone  bridge,  a  galvanometer,  two 
cells  of  battery  of  the  same  kind  and  size,  connecting  wires, 
and  one  dry  cell. 

Data.  — 


OBSERVATIONS 

RATIO 

OHMS 

VALUE 

RESIST- 
ANCE OF 

IN  Box 

OF  * 

ONE  CELL 

Case  i,  plates  —  normal 

Case  2,  plates  —  near  together 

Case  3,  plates  —  far  apart  .     . 

Directions.  —  Connect  the  apparatus  as  shown  in  Figure 
8.  Compare  this  diagram  with  the  one  given  in  Experi- 
ment 27  (Figure  6)  for  measuring  the  resistance  of  a  me- 
tallic conductor.  Do  you  find  any  essential  difference  ? 

Balance  the  bridge  as  you  would  in  measuring  any  ordi- 
nary resistance.  If  you  do  not  know  exactly  how  this  is 
done,  refer  to  the  directions  given  under  Experiment  27. 

Substitute  the  values  of  rv  r2,  an  d  R  in  the  equations  =  —  R 

r* 
and  calculate  the  value  of  x.     From  this  result  find  the 

internal  resistance  of  one  cell. 

In  the  foregoing  measurement  the  battery  plates  were 
in  their  normal  positions.  Now  measure  their  resistance, 
(a)  with  the  plates  as  near  together  as  possible,  (b)  with  the 
plates  as  far  apart  as  possible.  Record  all  results  in  the 
table. 


48 


PHYSICAL   LABORATORY   GUIDE 


FIG.  8. 

Conclusion.  —  Why  are  the  cells  placed  in  opposition  for 
this  experiment?  Explain  why  the  internal  resistance  of 
the  same  cell  should  have  different  values  in  the  three 
cases  which  you  have  investigated.  Reasoning  from  the 
data  you  have  obtained  in  this  experiment,  suggest  other 
things  that  would  affect  the  internal  resistance  of  a  cell. 


EXPERIMENT  29 

Object.  —  To  measure  the  internal  resistance  of  a  cell  of 
battery  by  Mance's  method. 

Apparatus.  —  A  Wheatstone  bridge,  a  galvanometer,  a 
small  Daniell  cell,  and  connecting  wires. 

Data.  —  Let  the  pupil  arrange  a  table  for  the  numerical 
results  of  this  experiment. 


ELECTRICAL   TESTING 


49 


Directions.  —  Connect  the  apparatus  as  shown  in  Figure 
9.  Compare  these  connections  with  those  you  made  in 
Experiment  27  when  you  used  the  Wheatstone  bridge  for 
regular  resistance  measurements. 

Now  depress  the  galvanometer  key  and  note  the  deflec- 
tion. While  holding  the  galvanometer  key  down,  depress 
the  battery  key,  also.  This  will  probably  change  the 
deflection.  Adjust  the  ratios  and  value  of  the  resistance 


FIG.  9. 

in  the  box  by  successive  trials  until  closing  the  battery  key 
does  not  change  the  deflection  of  the  galvanometer.  Com- 
pare this  condition  for  a  balanced  bridge  with  the  con- 
dition for  balance  when  the  bridge  is  used  in  ordinary 
resistance  measurements.  (See  Experiment  27.)  The 
values  of  rv  r2,  and  R  may  be  substituted  in  the  equation 


50  PHYSICAL   LABORATORY   GUIDE 

Conclusion.  —  In  the  practical  use  of  batteries,  is  the 
internal  resistance  of  a  cell  an  important  consideration  ? 
Why  ?  Explain  why  closing  the  battery  key  does  not 
change  the  deflection  when  the  bridge  is  properly  balanced 
for  this  experiment.  To  do  this,  give  careful  attention  to 
those  points  which  have  equal  potential. 


EXPERIMENT  30 

Object.  —  To  measure  the  internal  resistance  of  a  cell  of 
battery  by  the  Half-current  Method. 

Apparatus.  —  A  tangent  galvanometer  whose  resistance 
is  known,  a  small  Daniell  cell,  a  resistance  box,  a  contact 
key,  and  connecting  wires. 

Data.  — 


OBSERVATIONS 

TRIAL  i 

TRIAL  2 

Resistance  in  box  (r\)       
Deflection  :  larger  angle    
Tangent  of  larger  angle     
Resistance  in  box  (r2)       
Deflection:  smaller  angle       .     ... 
Tangent  of  smaller  angle  
Resistance  of  galvanometer  (g)  .     .     . 
Internal  resistance  of  cell  

Directions.  —  Connect  apparatus  as  shown  in  Figure  10, 
placing  the  galvanometer  in  the  magnetic  meridian.  By 
referring  to  the  table  of  natural  tangents  on  page  169,  select 
two  such  angles  that  the  tangent  of  one  is  just  twice  the 
tangent  of  the  other;  namely,  33  and  18. 


ELECTRICAL   TESTING 


Adjust  the  resistance  in  the  box  until  the  galvanometer 
shows  33°  west.  Record  the  number  of  ohms  in  box  and 
the  deflection.  Now  increase  the  resistance  in  the  box  until 
the  deflection  is  just  18°  west.  Again  record  the  ohms  in 


I 


© 1 


FIG.  10. 

box  and  the  deflection.  Obtain  the  resistance  of  the  gal- 
vanometer from  your  instructor.  Repeat  the  above  meas- 
urements for  Trial  2,  but  take  all  deflections  to  the  east 
this  time. 

In  a  tangent  galvanometer  the  current  strength  is  di- 
rectly proportional  to  the  tangent  of  the  angle  of  deflec- 
tion. Applying  this  principle,  together  with  Ohm's  law, 

we  have  : 

E  E 


=  2 


(       E       \ 

[  - 

\r<+     +  xJ 


x=r<i-2r-g  ......       (i) 

Substituting  in  equation  (i)  the  data  just  found,  the  in- 
ternal resistance  of  the  cell  may  be  calculated. 


PHYSICAL   LABORATORY   GUIDE 


The  result  obtained  from  the  data  of  Trial  i  should 
agree  closely  with  the  result  obtained  from  the  data  of 
Trial  2. 

Conclusion.  —  State  clearly  why  the  angles  chosen  for  the 
deflections  in  this  experiment  should  be  so  taken  that  the 
ratio  of  their  tangents  is  accurately  known.  The  work  is 
simplified  if  a  simple  ratio,  namely,  2  given  above,  is  used. 
State  Ohm's  law  and  explain  its  application  in  deducing 
Formula  (i). 

EXPERIMENT  31 

Object.  —  To  test  the  laws  of  resistance  for  metallic 
conductors. 

Apparatus.  —  A  Wheatstone  bridge,  a  galvanometer,  a 
dry  battery,  a  micrometer  caliper,  a  meter  stick,  a  copper 
wire  10  ft.  long,  German  silver  wires  10  ft.  long  and  20  ft. 
long  (all  three  wires  of  the  same  diameter),  and  a  German 
silver  wire  10  ft.  long  and  twice  the  diameter  of  the  others. 

Data.  — 


OBSERVATIONS 

GERMAN  SILVER 

COPPER 

i 

2 

3 

Length  of  wire  in  feet  .... 
Diameter  of  wire  in  mils  .     .     . 
Resistance  in  ohms      .... 
Specific  resistance  (calculated)  . 
Specific  resistance  (from  table)  . 

Directions.  —  Connect  the  Wheatstone  bridge  and  then 
make  the  measurements  called  for  by  the  table.     If  the 


ELECTRICAL   TESTING  53 

lengths  of  the  wires  are  marked,  these  may  be  acCepted 

and  recorded  in  the  table. 

If  fi  =  resistance  of  a  conductor  in  ohms, 

k  =  the  specific  resistance  in  ohms, 
/=  length  of  conductor  in  feet, 
d=  diameter  of  conductor  in  mils, 

then  (i)          ^  =  ^,or(2)£=^ 

Using  formula  (2),  calculate  the  specific  resistance  for 
each  wire. 

Compare  these  values  with  those  found  in  the  table  in 
the  Appendix.  Study  carefully  the  data  obtained  and 
note  the  effect  of  change  of  length,  diameter,  and  mate- 
rial upon  the  resistance. 

Conclusion.  —  State  the  laws  of  resistance.  Show  how 
closely  yo.ur  results  agree  with  these  laws.  Define  specific 
resistance. 

NOTE.  —  Refer  to  Experiment  27  for  diagram  of  connections  and 
instructions  -for  using  a  Wheatstone  bridge.  The  method  of  substi- 
tution explained  in  Experiment  25  may  be  used  in  place  of  the  Wheat- 
stone  bridge  for  this  experiment,  if  it  is  preferred. 


EXPERIMENT  32 

Object.  —  To  find  how  much  one  ohm  of  copper 
increases  in  resistance  when  heated  one  degree 
Centigrade. 

Apparatus.  —  A  Wheatstone  bridge,  a  galvanometer,  a 
coil  of  insulated  copper  wire  (see  Chap.  XII  (£)),  a  ther- 
mometer, a  calorimeter,  a  boiler,  a  burner,  and  connecting 
wires. 


54 


PHYSICAL   LABORATORY   GUIDE 


Data. 


OBSERVATIONS 

SYMBOL 

VALUE 

Resistance  of  coil,  cold     
Resistance  of  coil,  hot       

*. 
R. 

Temperature  of  coil  before  heating     . 
Temperature  of  coil  after  heating   .     . 
Temperature  coefficient  of  copper  .     . 

f*l 

ti 

fa 

Directions.  —  Connect  the  apparatus  and  measure  the 
resistance  of  the  conductor,  cold.  If  in  doubt,  refer  to 
Experiment  27  for  diagram  of  connections  and  directions 
for  using  the  Wheatstone  bridge. 

Take  the  temperature  of  the  air  as  the  temperature  of 
the  coil,  cold.  Pass  the  coil  and  thermometer  through  a 
large  cork  so  that  they  may  be  placed  in  the  calorimeter 
without  touching  it.  The  cork  serves  as  a  cover  for  the 
calorimeter.  The  bulb  of  the  thermometer  should  be  near 
the  center  of  the  coil.  Why  ?  Now  place  the  calorimeter 
in  the  boiler  and  heat  until  the  thermometer  reaches 
a  constant  temperature.  Before  turning  off  the  heat, 
again  measure  the  resistance  of  the  coil  and  record  its 
temperature. 

To  find  the  amount  one  ohm  of  copper  increases  in  re- 
sistance when  heated  one  degree  Centigrade,  or  its  temper- 
ature coefficient,  as  this  quantity  is  technically  called, 
substitute  the  observed  values  in  the  formula 

R  —  R 
Temperature  coefficient  =  — 2 — 

(>2-*i)*i 

Conclusion.  — Show  that  the  formula  given  is  correct  for 
temperature  coefficient.  Compare  your  result  with  the 
temperature  coefficient  of  copper  given  in  the  Appendix. 


ELECTRICAL   TESTING 


EXPERIMENT  33 


55 


Object.  —  To  measure  the  counter  e.  m.  f.  of  an  electric 
motor. 

Apparatus. — A  small  10- volt  shunt-wound  electric  motor 
(see  Chap.  XII),  a  voltmeter  ammeter,  sufficient  batteries 
to  give  10  volts,  or  a  5-ampere  lamp  bank  with  resistance 
coils  in  series  giving  10  volts  when  used  as  a  potentiometer 
(see  Chap.  XII).  This  is  more  satisfactory  than  the  bat- 
teries if  street  direct  current  is  available. 

Data.  — 


OBSERVATIONS 

Fall  of  potential  across  the  field  .                           .     . 

Current  through  the  field                                   * 

Calculated  resistance  of  the  field       ''.' 
Fall  of  potential  across  armature       ...... 
Current  through  armature  

Calculated  resistance  of  armature      .     .     .    '.'-.-.  ": 

Combined  resistance  of  field  and  armature     ,     .  .  !.; 
Impressed  e  m  f.  motor  runnin^     .                          ^ 

Current  drawn  by  motor  while  running      . 
Counter  e  m.  f  of  motor    ' 

Directions.  —  Measure  the  resistance  of  the  field  and  the 
armature  separately  by  the  fall  of  potential  method  as 
follows :  Connect  the  voltmeter  in  parallel  with  the  field 
and  the  ammeter  in  series  with  it  and  observe  the  readings 
carefully.  Substitute  the  values  just  obtained  in  Ohm's  law 
and  calculate  the  resistance  of  the  field.  Find  the  resist- 
ance of  the  armature  in  the  same  manner.  Now  find  the 
combined  resistance  of  field  and  armature  by  calculation 
(see  Chap.  XI,  page  170).  With  the  armature  and  field  con- 

PHYS.  LAB.  GUIDE  —  5 


56  PHYSICAL   LABORATORY   GUIDE 

nected  in  shunt,  measure  the  current  taken  and  the  e.  m.  f. 
impressed  upon  the  motor  while  it  is  running.  Substitute 
the  values  just  found  in  the  formula 

r  —  E~e 
~~ 


where  C  =  current  taken  to  run  motor. 
E  =  impressed  e.  m.  f. 
e  =  counter  e.  m.  f. 

R  =  combined   resistance   of  both   field  and  arma- 
ture in  parallel,  and  solve  for  e. 

Conclusion.  —  Explain  the  cause  and  use  of  the  counter 
e.  m.  f.  in  a  motor. 

EXPERIMENT  34 

• 

Object.  —  To  study  the  construction  and  control  of  a 
shunt-wound  electric  motor. 

Apparatus.  —  A  small  ic-volt  shunt-wound  electric  motor 
(see  Chap.  XII),  a  voltmeter,  batteries  to  give  10  volts  or 
special  lamp  bank  (see  Chap.  XII)  if  street  direct  current 
is  available,  a  compass  (magnetic),  a  resistance  box,  and  a 
small  screw  driver. 

Directions.  —  Remove  the  pulley  from  the  armature  shaft, 
unscrew  the  bearing,  and  withdraw  the  armature  carefully. 
Pass  a  small  current  through  the  field  coil  and  test  the  po- 
larity of  the  magnet.  Make  a  diagram  of  the  motor  in  your 
notebook  and  mark  the  poles  just  tested.  In  like  manner 
test  the  armature  for  poles  with  the  compass.  The  current 
should  pass  into  the  armature  through  diametrically  oppo- 
site points  on  the  commutator.  Mark  the  armature  poles 
on  the  diagram,  also. 


ELECTRICAL   TESTING  57 

Now  carefully  reassemble  the  motor  and  start  it  running 
as  slowly  as  possible.  Regulate  its  speed  by  using  the 
smallest  number  of  batteries  or  lamps  on  the  lamp  bank, 
which  will  give  voltage  enough  to  operate  the  motor.  Meas- 
ure this  pressure  with  a  voltmeter.  Now  gradually  increase 
the  speed  of  the  motor  by  putting  more  batteries  or  lamps 
in  circuit.  Note  the  readings  of  the  voltmeter  for  each 
change  of  the  speed  of  the  motor. 

Connect  a  resistance  box  in  series  with  the  armature  of 
the  motor  only,  and  while  it  is  running  remove  the  I,  2,  3, 
5,  and  10  ohms  plugs  in  succession,  noting  carefully  the 
change  produced  each  time  in  the  speed  of  the  motor. 

Next  connect  the  resistance  box  in  series  with  the  field 
of  the  motor  only  and  remove  the  I,  2,  3,  5,  and  10 
ohms  plugs  in  succession,  noting  again  the  effect  upon  its 
speed. 

Arrange  the  connections  so  that  the  motor  runs  in  the 
reverse  direction. 

Conclusion.  —  Explain  why  the  armature  of  an  electric 
motor  revolves.  State  the  effect  produced  upon  the  speed 
of  the  motor  and  the  reason  for  it  in  each  of  the  following 
cases : 

I.   When  the  voltage  is  changed. 
II.    When  resistance  is  put  in  series  with  the  armature. 

III.    When  resistance  is  placed  in  series  with  the  field. 

Does  reversing  the  potential  on  a  shunt-wound  motor 
cause  it  to  runv  backwards  ?  Why  ? 

If  you  have  previously  performed  Experiment  33,  then 
explain  the  relation  of  the  counter  e.  m.  f.  of  the  motor  to 
each  of  the  cases  I,  II,  and  III  just  considered. 

What  are  the  relative  advantages  of  high  and  low  speed 
motors  of  the  same  power  ? 


PHYSICAL   LABORATORY   GUIDE 


EXPERIMENT  35 
Object. —  To  study  the  direct  current  dynamo. 

Apparatus.  —  Two  small  shunt-wound  direct  current 
motors  (see  Chap.  XII),  a  voltmeter,  an  ammeter,  a 
rubber  band  or  very  small  leather  belt,  a  lo-volt  battery  or 
a  potentiometer  lamp  bank  (see  Chap.  XII),  and  a  resist- 
ance box. 

Data.  — 


OBSERVATIONS 

SELF 
EXCITED 

SEPARATELY 
EXCITED 

E.  M.  F.  used  upon  the  motor    .     .     . 
Amperes  drawn  by  motor  
Watts  consumed  by  motor     .... 
E.  M.  F.  generated  by  dynamo  .     .     . 
Current  drawn  from  dynamo  .... 
Watts  output  of  dynamo    
Efficiency  of  the  transformation 

Directions.  — Belt  the  motor  and  dynamo  together.  Use 
as  high  an  e.  m.  f.  as  possible  on  the  motor  and  measure 
the  volts  and  amperes  consumed  by  motor  and  generated 
by  the  dynamo.  Do  this  with  the  dynamo,  exciting  its  own 
field  and  also  with  its  field  separately  excited.  Record 
both  sets  of  data. 

Use  the  resistance  box  as  a  load  for  the  dynamo,  ad- 
justing the  plugs  until  the  dynamo  gives  its  greatest 
output. 

Calculate  the  watts  used  by  the  motor  and  generated 
by  dynamo  in  both  cases.  Account  for  the  difference  in 
results. 


ELECTRICAL   TESTING  59 

The  watts  drawn  from  the  dynamo  divided  by  the  watts 
put  into  the  motor  gives  the  efficiency.  Express  this  in 
percentage  form. 

Conclusion.  —  State  the  principle  upon  which  a  dynamo 
works.  Name  the  principal  parts  of  a  dynamo  and  state 
briefly  the  function  of  each  part.  If  the  energy  put  into 
and  taken  out  of  the  motor  and  dynamo,  respectively,  is  not 
equal,  account  for  this  apparent  loss  of  energy. 


CHAPTER   VI 

THE   MECHANICS   OF   SOLIDS 
EXPERIMENT  36.    PART  1 

Object.  —  To  find  how  the  bending  of  a  beam  varies 
(a)  with  the  load,  (&)  with  the  length. 

Apparatus.  —  A  wooden  strip  1.5  x  1.5  cm.  cross  section 
and  100  cm.  long,  means  for  supporting  one  end  firmly,  a 
vertical  scale,  a  scalepan,  and  a  set  of  weights. 

Data.  — 


LENGTH 
OF  BEAM 

LOAD  IN 
GRAMS 

SCALE  READING 
WITHOUT  LOAD 

SCALE  READING 
WITH  LOAD 

DEFLECTION 

, 

Directions.  —  Arrange  the  apparatus  as  shown  in  Fig- 
ure ii.  Using  a  beam  75  cm.  long  (from  support  to  scale- 
pan)  read  the  position  of  the  upper  edge  of  beam  against 
the  vertical  scale.  Place  100  gm.  in  the  scalepan  and 
again  read  the  scale.  Subtract  the  first  from  this  second 
reading  to  find  the  deflection.  In  like  manner  make  read- 
ings every  100  gm.  until  a  load  of  500  gm.  is  reached. 

60 


THE   MECHANICS   OF    SOLIDS 


6l 


Next,  using  a  constant  load  of   500  gm.,  find  the  de- 
flection when  the  beam  is  15,  30,  45,  60,  and  75  cm.  long. 


e      e 


e      e 
e 


FIG.  ii. 

Record  all  numerical  data  in  a  table,  as  shown. 

Now  look  the  data  over -carefully  and  decide  how  the 
bending  varies  with  the  load  and  with  the  length.  It  is 
obvious  that  increasing  either  of  these  quantities  increases 
the  deflection ;  hence  the  deflection  varies  directly  both 
with  the  load  and  with  the  length.  However,  it  may  vary 


62  PHYSICAL   LABORATORY   GUIDE 

as  the  square  or  cube  or  fourth  power  of  the  length. 
To  settle  this  point,  note  the  deflection  when  the  beam  is 
30  cm.  long  and  again  when  it  is  twice  this  length  (60  cm.). 
Is  the  deflection  twice  as  much  when  the  length  is  doubled  ? 
Is  it  four  times  as  much  (22  =  4)  ?  Or  is  it  eight  or  sixteen 
times  as  much  (23  =  8  and  24  =  16)  ? 

Conclusion.  —  Write  the  two  laws  for  the  bending  of 
beams.  Does  your  data  agree  exactly  with  these  laws  ? 
Why  ?  State  Hooke's  law.  Compare  it  with  your  first 
law  for  beams.  What  are  some  of  the  probable  sources 
of  error  in  your  work  ? 

Suggestion.  — -  If  time  permits,  this  experiment  may  be 
made  to  cover  the  third  and  fourth  laws  of  beams,  as  fol- 
lows :  Using  a  length  of  75  cm.  and  a  load  of  500  gm., 
place  two  precisely  similar  beams  side  by  side  and  with  the 
scalepan  resting  on  both.  Note  the  deflection.  Compare 
this  with  a  single  beam  under  the  same  conditions  and 
state  how  the  deflection  varies  with  the  width  of  beam. 

Next,  place  the  two  beams  in  the  support,  one  below 
the  other,  and  again  load  with  500  gm.,  using  a  length  of 
75  cm.  Comparing  this  result  with  the  corresponding 
one  for  a  single  beam  will  enable  you  to  state  the  fourth 
law,  i.e.  how  the  deflection  of  a  beam  varies  with  the 
depth.  The  two  beams  are  readily  held  together  with 
rubber  bands. 

EXPERIMENT  36.    PART  2 

Object.  —  To  plot  two  curves  on  one  sheet  of  section 
paper  to  show  the  laws  of  beams. 

Directions. — Use  the  data  obtained  in  Part  I.  Draw 
axes  of  X  and  Y  with  origin  in  the  lower  left-hand  corner 


THE   MECHANICS   OF   SOLIDS  63 

of  the  paper.  Plot  the  weights  and  the  lengths  of  beam 
used  in  the  two  cases  along  the  axis  of  X  and  the  corre- 
sponding deflections  produced  along  the  axis  of  Y. 

Use  any  convenient  scale  of  such  a  size  that  the  curves 
when  drawn  will  almost  fill  the  paper.  The  scale  is  easily 
decided  upon  by  dividing  the  total  number  to  be  plotted 
along  a  given  axis  by  the  number  of  units  of  length  of 
that  axis,  or  vice  versa.  This  quotient  will  probably  be  a 
fractional  number.  Choose  the  whole  number  nearest  to 
this  as  the  scale. 

It  is  better  to  plot  and  draw  one  curve  completely  before 
attempting  the  second.  Consult  Experiment  5  ("  To  study 
the  curve  as  a  method,"  etc.),  if  further  details  of  the 
method  of  plotting  curves  are  required. 

Conclusion.  —  If  two  quantities  are  directly  proportional, 
will  their  graph  be  a  straight  line  or  a  curved  line  ?  Is 
this  always  so  ?  Why  are  very  long  spans  for  bridges 
difficult  to  construct  ? 

Suggestion.  —  If  Part  2  is  used,  it  may  well  be  recorded 
as  a  separate  experiment.  Two  laboratory  periods  of  the 
usual  length  will  be  necessary  to  complete  both  parts. 

EXPERIMENT  37 

Object.  —  To  test  the  parallelogram  law  for  two  con- 
current forces. 

Apparatus.  —  Three  spring  balances  (0-250  gm.)  with 
holders  for  use  in  a  horizontal  position,  drawing  com- 
passes, a  3O-cm.  metric  scale,  a  piece  of  thread  and 
some  pins,  and  a  rectangular  wooden  block. 


64  PHYSICAL  LABORATORY   GUIDE 

Directions.  —  Cut  the  thread  into  three  pieces  of  equal 
length.  Fasten  together  three  of  the  ends  —  one-  end  of 
each  piece.  Make  loops  in  the  free  ends  and  attach  a 
balance  to  each.  Arrange  two  of  the  balances  to  act  as 
components  and  the  third  as  an  equilibrant.  Put  tension 
on  all  three  and  do  not  have  any  reading  less  than 
100  gm.  Hold  the  balances  in  position  either  with  clamps 
and  cords  from  the  edge  of  the  table,  or  by  driving  pins 
into  the  table.  Care  should  be  taken  that  the  draw  bar 
of  the  balance  does  not  touch  either  side  of  the  slot 
through  which  the  index  runs,  as  this  would  introduce  a 
serious  friction  error.  The  draw  bar  and  thread  should 
be  in  the  same  straight  line.  Why  ?  Place  a  sheet  of 
notebook  paper  under  the  threads  and  in  such  a  position 
that  the  point  of  application  of  the  three  forces  comes  near 
one  corner  of  the  paper.  Place  two  dots  under  each  thread 
to  indicate  the  directions  of  the  forces.  This  is  best  done 
by  placing  one  edge  of  the  rectangular  wooden  block 
parallel  to  one  of  the  strings  and  as  near  as  possible  to  it 
without  touching  it.  While  in  this  position  draw  a  short 
line  along  the  edge  of  the  block.  This  will  be  directly 
under  the  thread  if  the  work  is  carefully  done.  If  this  is 
done  at  both  ends  of  each  thread,  their  directions  will  be 
accurately  recorded.  Read  the  balances  and  record  the 
results  in  each  case,  between  the  dots  just  drawn. 

Remove  the  tension  from  the  balances  and  note  whether 
they  read  correctly  or  not  at  zero.  If  there  is  an  error, 
add  or  subtract  this,  as  the  case  may  be,  to  the  readings 
under  tension. 

Using  any  convenient  scale,  such  as  one  millimeter 
equals  one  gram,  construct  a  parallelogram  upon  these 
components  as  sides,  drawing  the  lines  showing  their 
directions  through  the  points  just  found.  Measure  its 


THE   MECHANICS    OF   SOLIDS 


concurrent  diagonal  and  compare  its  value  in  grams  with 
the  equilibrant  force. 

Conclusion.  —  State  the  parallelogram  law.  What  re- 
lation should  exist  between  the  resultant  found  above  and 
the  reading  of  the  equilibrant  balance  ?  What  relation 
does  exist  in  your  result  ?  Does  this  prove  or  disprove 
the  law  ? 

EXPERIMENT  38 
Object.  —  To  test  the  laws  of  parallel  forces. 

Apparatus.  —  Two  spring  balances  (0-250  gm.),  a 
meter  stick,  a  2OO-gm.  weight,  a  3O-cm.  rule,  and  some 
thread. 

Data.  — 


u 

FORCE 

MAGNITUDE  OF 
FORCE 

POINT  OF 
APPLICATION 

1  DIRECTION 

MOMENT  OF 
FORCE 

Observed 

Corrected 

Symbol 

Position 

Arm 

Fulcrum 

Value 

h-  1 

Component  I 
Component  II 
Equilibrant 

H 

Component  I 
Component  II 
Equilibrant 



S 

Component  I 
Component  II 
Equilibrant 

Directions.  —  Hang  the  balances  to  the  crossbar  of  tho 
table,  just  96  cm.  apart.     Attach  a  meter  stick  to  the  bal- 


66  PHYSICAL   LABORATORY   GUIDE 

ances  by  means  of  threads,  with  slipknots  for  adjustment. 
The  threads  should  be  just  2  cm.  from  the  ends  of  the 
stick.  By  means  of  another  thread  fasten  the  2OO-gm. 
weight  to  the  stick,  using  rather  a  large  hoop. 

For  Case  I  place  the  weight  at  the  middle  point  of  the 
bar.  The  bar  should  be  made  horizontal  by  adjusting  the 
threads. 

In  Case  2  hang  the  weight  from  the  34-cm.  mark. 

In  Case  3  it  should  be  suspended  74  cm.  from  the 
end  of  the  bar. 

The  bar  should  be  horizontal  before  any  observations 
are  made.  Take  the  observations  called  for  by  the  table, 
making  all  measurements  of  position  from  the  zero  end  of 
the  meter  stick.  Remember  that  the  arms  of  the  forces 
are  the  perpendicular  distances  from  the  lines  of  action  of 
the  forces  to  the  axis  about  which  moments  are  taken. 

Remove  the  2OO-gm.  weight  and  note  the  balance 
readings  under  the  weight  of  the  meter  stick  alone.  De- 
duct these  values  in  each  case  from  the  observed  balance 
readings  to  obtain  the  corrected  readings.  These  values 
are  then  the  components  of  the  2OO-gm.  equilibrant. 

In  Case  I  take  moments  about  the  5<D-cm.  division 
(point  of  application  of  the  equilibrant) ;  in  Case  2  about 
the  5-cm.  point ;  in  Case  3  about  any  point  in  the  bar  you 
choose. 

Make  a  diagram  of  the  apparatus  and  letter  the  points 
of  application  of  the  forces.  Record  these  in  the  column 
headed  Symbol. 

Conclusion.  —  Compare  the 'sum  of  the  components  with 
the  value  of  the  equilibrant  in  each  case.  Note  the  pro- 
portion that  exists  between  the  component  forces  and  the 
parts  of  the  line  joining  them.  It  is  divided  into  these 


THE   MECHANICS   OF   SOLIDS  67 

parts  by  the  point  of  applications  of  the  equilibrant  in 
each  case.  Is  this  proportion  direct  or  inverse?  Now 
state  the  laws  of  parallel  forces. 

Next  compare  the  sum  of  the  moments,  trying  to  pro- 
duce motion  clockwise  with  those  making  the  same  effort 
in  a  counterclockwise  direction  in  each  case.  With  this 
help  state  the  general  law  of  moments  for  a  body  in 
equilibrium.  In  applying  the  law  of  moments,  does  it 
make  any  difference  where  you  take  the  axis  about  which 
the  moments  are  figured  ? 

EXPERIMENT  39 

Object.  —  Given  one  known  weight,  to  find  the  center  of 
gravity  and  weight  of  a  lever. 

Apparatus.  —  A  meter  stick,  a  wooden  knife  edge,  a 
platform  scale,  a  set  of  weights,  a  rectangular  block,  and 
a  piece  of  thread. 

Data.  — 


OBSERVATIONS 


Position  of  center  of  gravity  of  meter  stick     . 

Position  of  loo-gm.  weight 

Fulcrum  when  meter  stick  and  weight  balance 

Arm  of  loo-gm.  weight 

Arm  of  resultant  acting  at  center  of  gravity    . 

Moment  of  the  loo-gm.  weight 

Moment  of  x  (the  weight  of  the  lever)  .     ,     . 
Weight  of  the  lever  —  by  moments  ., 
Weight  of  the  lever  —  by  platform  scale    .     . 


Directions.  —  Balance  the  meter   stick    upon    the  knife 
edge  to  determine  its  center  of  gravity.     Since  the  stick  is 


68  PHYSICAL  LABORATORY  GUIDE 

in  unstable  equilibrium,  that  point  should  be  chosen  as  the 
center  of  gravity  at  which  it  appears  most  nearly  to  balance 
when  in  a  horizontal  position.  Give  the  reason  for  this 
unstable  equilibrium.  Place  the  knife  edge  on  the  rectan- 
gular block.  Suspend  the  roo-gm.  weight  from  the  meter 
stick  near  one  end  by  means  of  a  loop  of  thread  and  then 
find  the  position  where  the  stick  will  balance  on  the  knife 
edge. 

Record  all  distances  in  centimeters,  measuring  from  the 
zero  end  of  the  meter  stick.  Calculate  the  arms  of  the 
forces.  Remember  that  it  is  immaterial  when  making  a 
calculation  whether  the  components  or  their  resultant  are 
considered.  As  the  number  of  parallel  component  forces 
of  gravity  is  as  great  as  the  number  of  molecules,  it  is  far 
more  convenient  in  this  experiment  to  consider  the  resultant 
(the  sum  of  all  these  component  forces)  instead  of  the  com- 
ponents. This  resultant  acts  at  the  center  of  gravity  of 
the  stick.  Why  ? 

In  applying  the  general  law  of  moments  in  this  case, 
two  forces  must  be  considered  —  the  loo-gm.  weight  and 
the  weight  of  the  stick.  From  the  application  of  this  law, 
calculate  the  weight  of  the  lever.  Next,  weigh  it  on  the 
platform  scale  and  compare  these  values. 

Conclusion.  —  Define  center  of  gravity.  Explain  why 
the  point  about  which  the  bar  balances  is  its  center  of 
gravity.  State  the  general  law  of  moments.  Why  must 
the  bar  be  so  carefully  balanced  before  applying  this 
law? 

This  experiment  suggests  a  method  for  finding  the 
approximate  weight  of  logs  or  other  large  objects.  In  this 
case,  the  experimenter's  weight  could  be  used  in  place  of 
the  100  gm.  weight  of  this  experiment. 


THE   MECHANICS   OF    SOLIDS 


69 


EXPERIMENT  40 

Object.  —  To   test   the   laws   of   vibration   for  a  simple 
pendulum. 

Apparatus.  —  A  small  iron  weight,  a  thread,  a  piece  of 
beeswax,  a  meter  stick,  a  ruler,  and  a  cork  stopper. 

Data.  — 


LENGTH  OF 

NUMBER  OF 

TIME  OF  ONE 

SQUARE  Roor 

COLUMN  (4) 

CASE 

PENDULUM 
IN  CM. 

VIBRATIONS 
IN  i  MINUTE 

VIBRATION 
IN  SECONDS 

OF  THE 

LENGTH 

DIVIDED 
BY  (3) 

(i) 

(2) 

(3) 

(4) 

(5) 

I 

II 

I 

III 

Directions. — Wax  the  thread  thoroughly  to  prevent  it 
from  twisting  and  to  increase  its  strength.  Drive  a  wire 
nail  with  a  small  head  into  the  adjustable  crossbar  of  the 
laboratory  table.  Make  a  deep  cut  across  one  end  of  the 
cork  and  force  it  over  the  wire  nail.  Attach  the  iron 
weight  to  one  end  of  the  thread  and  pass  the  other  through 
the  slot  in  the  cork.  It  is  now  very  easy  to  adjust  it  to 
any  required  length. 

I.  With  a  length  o'f  one  meter  measured  from  the  under 
side  of  the  cork  to  the  estimated  center  of  gravity  of  the 
weight,  time  its  vibrations  for  one  minute,  using  first  a 
very  small  arc,  then  a  medium  arc,  and,  last,  as  large  an  arc 
as  possible.  If  you  are  in  doubt  as  to  the  result,  repeat 
timing  for  two  minutes  instead  of  one. 


70  PHYSICAL   LABORATORY   GUIDE 

2.  Using  a  small  amplitude  of  vibration,  adjust  the  pen- 
dulum in  turn  to  lengths  of  100,  64,  36,  and  16  cm.     Com- 
pare the  values  found  in  column  (5)  and  decide  how  the 
time  of  one  vibration  is  affected  by  the  length. 

3.  Place  the  pole  of  a  strong  bar  magnet  on  the  table 
and  adjust  the  pendulum  so  that  the  bob  just  clears  it  by  a 
small  margin.     Adjust  the  pendulum,  using  two  or  more  of 
the  same  lengths  as  those  experimented  with  in  Case  2. 
How  does  the  time  of  one  vibration  under  these  conditions 
compare  with  the  time  for  the  same  pendulum  length  in 
Case  2  ? 

The  effect  of  the  magnet  is  the  same  as  an  increase  in 
the  acceleration  of  gravity  (g.).  This  data  checks  the  third 
law  of  the  pendulum. 

It  is  not  necessary  to  work  out  the  values  called  for  in 
columns  (4)  and  (5),  if  your  time  is  limited,  except  in 
Case  2. 

Conclusion.  —  Write  three  laws  for  the  pendulum.  Dis- 
tinguish between  a  simple  and  a  compound  pendulum. 
Which  have  you  been  using  ?  Does  this  experiment  fully 
demonstrate  the  truthfulness  of  all  three  laws  ? 

EXPERIMENT  41 

Object.  —  To  find  the  breaking  strength  of  several  wires 
and  to  calculate  the  tensile  strength  per  square  inch  for 
each  material  tested. 

Apparatus.  —  A  dynamometer  (0-30  lb.),  one  meter  each 
of  annealed  iron  wire,  copper  wire  (soft),  copper  wire 
(hard  drawn),  brass  wire,  steel  piano  wire  (28  B.  &  S.  gauge 
is  a  convenient  size),  a  micrometer  caliper,  and  a  30  cm. 
rule.  (A  testing  machine  is  desirable,  but  not  essential.) 


THE   MECHANICS   OF   SOLIDS 


Data.  — 


KIND  OF  WIRE 

DIAMETER 
IN  INCHES 

POUNDS  REQUIRED 
TO  BREAK  WIRE 

TENSILE  STRENGTH 
PER  SQUARE  INCH 

Directions.  —  If  a  testing  machine  is  not  used,  fasten  one 
end  of  the  wire  to  some  firm  support  such  as  a  gas  pipe  on 
the  laboratory  table  and  the  other  end  to  the  hook  of  the 
dynamometer.  Care  must  be  taken  to  avoid  kinks  or  sharp 
bends  in  the  wire,  as  these  would  introduce  points  of  weak- 
ness. A  two-way  connector  such  as  is  used  in  making 
electrical  circuits,  if  attached  to  the  balance  hook  by  a  stout 
wire  (see  drawing),  makes  an  excellent  surface  over  which 
to  wind  several  turns  of  the  wire.  The  short  end  of 
the  wire  is  readily  clamped  'under  one  of  the  binding 
screws. 

Measure  the  diameters  of  all  wires  with  the  micrometer 
caliper.  Make  at  least  two  trials  for  each  and  record  the 
average  value. 

Now  put  tension  on  one  of  the  wires.  Increase 
this  tension  slowly  until  the  wire  breaks,  and  record 
its  strength.  Test  all  the  wires  in  the  same  way.  Cal- 
culate the  cross-sectional  area  of  the  wires  in  square 
inches. 

The  following  direct  proportion  is  approximately  true : 
Cross-sectional  area  of  wire  in  square  inches  -*-  one  square 
inch  =  the  strength  of  the  wire  -*-  the  tensile  strength  of 
the  material  per  square  inch.  Why  is  this  true  ?  Calculate 

PHYS.  LAB.  GUIDE 6 


PHYSICAL  LABORATORY   GUIDE 


c::: 


FIG.  12. 


the    tensile    strength   per   square  inch   for  each  material 
tested. 

Conclusion.  —  Compare  these  tensile  strengths  with  those 
given  in  the  Appendix,  which  were  obtained  by  testing 
bars  one  square  inch  in  cross  section.  Are  your  results 
larger  or  smaller  than  those  in  the  Appendix?  Why? 
What  is  surface  tension  in  liquids  ?  Could  this  phenomenon 
exist  in  a  wire?  If  so,  what  would  be  its  effect  on  the 
comparative  strength  of  the  wires  and  the  bars  of  cross- 
sectional  area  equal  to  one  square  inch  ? 


THE   MECHANICS   OF   SOLIDS 


73 


EXPERIMENT  42 

Object.  —  To  measure  the  elasticity  of  a  steel  wire  and 
to  determine  the  elastic  limit  and  modulus  of  elasticity  for 
this  substance. 

Apparatus.  —  Steel  wire  (28  B.  &  S.  gauge),  at  least 
2  m.  long,  a  dynamometer  (0-30  lb.),  a  paper  index, 
sealing  wax,  a  3O-cm.  scale,  a  micrometer  caliper. 

Data.  — 


STRESS  IN 
POUNDS 

TEMPORARY 
ELONGATION 

PERMANENT 
ELONGATION 

ELONGATION 
PER  UNIT  FORCE 

Directions.  —  Attach  one  end  of  the  wire  firmly  to  a 
stationary  support  and  the  other  end  to  the  hook  of  bal- 
ance. Special  pains  must  be  taken  to  avoid  sharp  turns, 
kinks,  or  any  possibility  of  the  wire  slipping,  even  the 
smallest  amount.  (See  suggestion,  Experiment  41.) 

Near  the  balance  attach  a  paper  index  to  the  wire  with 
sealing  wax.  The  edge  of  the  paper  should  be  at  right 
angles  to  the  wire.  Place  the  3O-cm.  rule  under  the  index 
parallel  to  the  wire.  Put  two  pounds  of  tension  on  the 
balance.  Arrange  the  scale  so  that  some  even  division 
coincides  with  an  edge  of  the  index.  Now  increase  the 
tension  to  three  pounds  and  note  the  elongation.  Again 
bring  the  tension  back  to  two  pounds  and  note  whether 
there  is  any  permanent  stretch  to  the  wire.  Proceed  in 


74  PHYSICAL   LABORATORY   GUIDE 

this  way,  increasing  the  tension  one  pound  each  time  until 
the  elastic  limit  is  observed,  then  increase  the  tension  two 
pounds  on  each  trial  until  the  wire  breaks  or  the  limit  of 
the  balance  is  reached.  At  no  time  during  the  test  should 
the  tension  on  the  wire  be  less  than  two  pounds.  This 
will  avoid  any  slipping  or  kinking  of  the  wire.  Measure 
the  diameter  of  the  wire  and  calculate  its  cross  section. 
From  the  elastic  limit  for  this  wire  and  its  cross-sectional 
area,  calculate  the  elastic  limit  of  steel  for  a  bar  one  square 
inch  in  cross  section  (see  last  experiment). 

The  modulus  of  elasticity  is  that  theoretical  force  which 
would  double  the  length  of  a  bar  of  the  material  provided  it 
would  stand  such  an  elongation  without  rupture.  Average 
the  values  in  the  last  column  of  the  table,  using  only  those 
within  the  elastic  limit.  Divide  this  average  elongation  per 
pound  of  stress  by  the  length  of  the  wire  measured  in  the 
same  unit.  This  will  give  the  increase  in  length  per  unit 
of  length  for  one  pound  of  stress.  If  this  value  is  now  sub- 
stituted in  the  proportion  —  Elongation  per  unit  of  length 
for  one  pound  :  one  unit  of  length  =  one  pound  :  modulus 
of  wire,  the  modulus  of  the  wire  may  be  found.  Knowing 
how  many  times  the  cross  section  of  this  wire  is  contained 
in  one  square  inch,  the  modulus  of  elasticity  for  a  bar  one 
square  inch  in  cross  section  is  easily  found.  This  is  the 
usual  way  of  expressing  this  quantity. 

Conclusion.  —  State  the  elastic  limit  and  modulus  of 
elasticity  both  for  this  wire  and  for  a  bar  of  the  same 
material,  one  square  inch  in  cross  section.  Compare  these 
values  with  those  given  in  the  Appendix.  Account  for 
any  difference.  Arrange  all  these  values  in  a  table. 
State  Hooke's  law.  Does  it  apply  to  the  wire  just  tested  ? 
If  so,  to  what  extent  ? 


THE   MECHANICS   OF   SOLIDS 


EXPERIMENT  43 

Object.  —  To  test  the  laws  of  sliding  friction,  and  to  find 
the  coefficient  of  friction  for  the  two  given  surfaces. 

Apparatus.  —  A  pane  of  glass  (9"  x  24"),  a  rectangular 
block,  thread,  a  spring  balance  (o  -250  gm.),  a  set  of 
metric  weights,  a  bottle  of  alcohol,  tissue  paper,  and  a 
metric  scale. 

Data.  — 


OBSERVATIONS 

WEIGHT  OF 
BLOCK 

WEIGHT 
PLACED  UPON 
BLOCK 

AREA  OF 
RUBBING 
SURFACE 

READING  OF 
DYNAMOMETER- 
FRICTION 

Slow  speed 

High  speed 

Mod.  speed 

• 

Mod.  speed 

Mod.  speed 

Mod.  speed 

Mod.  speed 

Directions.  —  Clean  the  surface  of  the  glass  thoroughly 
with  alcohol  and  tissue  paper.  Use  a  loop  of  thread  to 
attach  the  balance  to  the  block.  Weigh  the  block.  Place 
100  gm.  on  the  block  and  draw  it  slowly  across  the  glass 
plate.  As  the  reading  of  the  dynamometer  is  apt  to  vary 
considerably,  estimate  its  average  reading  and  jot  down 
the  result  on  scratch  paper.  Make  a  number  of  trials 
under  these  conditions,  recording  each  one  on  scratch 
paper.  Average  these  readings  and  place  the  result  in 
the  table  as  the  first  item.  Repeat  at  a  much  higher 
speed.  Do  not  consider  the  first  heavy  pull  on  the  bal- 
ance required  to  accelerate  the  block,  but  only  the  force 


76  PHYSICAL   LABORATORY   GUIDE 

required  to  keep  it  in  motion.  Again  try  the  experiment 
at  moderate  speed.  Each  record  must  be  the  average  of 
several  trials.  Using  the  same  weight  and  a  moderate 
speed,  experiment  with  the  block  resting  on  its  smallest 
face. 

Now  go  back  to  the  large  face  in  contact  with  the  glass 
and  experiment,  first,  with  no  weight  on  the  block,  then 
with  its  own  weight  added  to  the  block  and  test  the  fric- 
tion. Next  add  double  its  weight,  and  so  on,  each  time 
using  a  moderate  speed  and  keeping  the  same  surface  in 
contact  with  the  glass. 

You  have  now  tried  (i)  three  different  speeds,  (2)  two 
areas  of  rubbing  surface,  and  (3)  five  different  pressures 
between  the  surfaces  in  contact.  In  each  case,  but  one 
quantity  was  allowed  to  vary,  while  the  others  were  kept 
constant. 

Conclusion.  —  Define  friction.  From  a  careful  study  of 
your  data,  write  three  laws  for  sliding  friction,  stating  in 
( i)  its  relation  to  velocity  ;  in  (2)  its  relation  to  area  of  rub- 
bing surface,  and  in  (3)  how  the  friction  varies  with  the  load. 
Define  coefficient  of  friction.  From  the  last  five  readings 
recorded  in  the  table,  calculate  the  values  of  this  coefficient 
and  average  them.  Take  this  as  the  coefficient  of  friction 
for  these  surfaces. 

EXPERIMENT  44 

Object. — To  plot  the  path  of  a  projectile  fired  horizon- 
tally with  a  velocity  of  100  ft.  per  second,  from  a  point 
256  ft.  above  the  ground. 

Apparatus.  —  Millimeter  section  paper,  a  straightedge. 


THE   MECHANICS   OF   SOLIDS 


77 


Data.  — 


T 

S  =VT 

s  =  JGT 

T 

s  =  VT 

S  =  $GT 

Directions.  — The  motion  of  this  projectile  is  a  resultant 
of  two  components  at  right  angles.  The  horizontal  com- 
ponent is  due  to  the  inertia  of  the  projectile  after  leaving 
the  gun,  and  hence  its  motion  is  uniform.  See  'Newton's 
first  law  of  motion.  The  vertical  component  is  caused  by 
gravity,  a  constant  force  acting  upon  the  projectile,  and 
therefore  its  motion  is  uniformly  accelerated. 

Calculate  the  space  passed  in  ^,  i,  i-J  seconds,  etc.,  for 
the  horizontal  component,  using  the  formula  s  —  vt,  and 
for  the  vertical  component  using  the  formula  s  =  \  gfi. 
Write  the  results  in  the  table. 

Draw  axes  of  X  and  Y  parallel  to  the  upper  and  left-hand 
edges  of  the  section  paper.  These  axes  should  coincide 
with  some  even  centimeter  division  near  the  edges  of  the 
paper. 

Plot  the  horizontal  components  of  the  projectile's  mo- 
tion along  the  axis  of  X,  using  some  convenient  scale  (i 
millimeter  — 2  feet)  and  the  vertical  component  along  the 
axis  of  Y. 

It  is  evident  that  the  projectile  at  the  end  of  the  first  half 
second  must  be  somewhere  on  a  vertical  line  drawn  through 
the  first  point  plotted  on  the  axis  of  X.  It  must  also  be  on 
a  horizontal  line  passing  through  the  first  point  plotted  on 
the  axis  of  Y.  If  both  of  these  lines  contain  the  point,  it 


PHYSICAL   LABORATORY   GUIDE 


must  be  at  their  intersection.  In  like  manner  determine 
the  other  points  in  the  projectile's  path  and  draw  a  smooth 
curve  from  the  origin  connecting  these  points.  This 
curve,  called  a  parabola,  is  the  path  of  the  projectile. 

Conclusion.  —  If  both  the  components  in  this  experiment 
had  a  uniform  motion,  how  would  you  find  the  resultant 
path?  State  the  law.  Why,  when  a  projectile  is  fired 
horizontally,  is  its  vertical  component  the  same  as  the 
motion  of  a  falling  body?  (Consult  Newton's  second  law 
of  motion.) 

NOTE.  —  Let  g  =  32  ft.  per  second  per  second.  Or,  better,  let  g  =  32 
ft.  per  (second)2. 

EXPERIMENT  45 
Object.  —  To  test  Boyle's  law. 

Apparatus.  —  A  Boyle's  law  tube,  mercury,  a  barometer, 
a  meter  stick. 

Data.  — 


(l) 

HEIGHT  OF 
MERCURY  IN 
SHORT  ARM 

(2) 

HEIGHT  OF 
MERCURY  IN 
LONG  ARM 

(3) 

LENGTH  OF 
CONFINED 
AIR  COLUMN 

(4) 

LENGTH  OF 
EFFECTIVE 
MERCURY 
COLUMN 

(5) 
TOTAL 
LENGTH  OF 
MERCURY 

CAUSING 

PRESSURE 

(6) 

PRODUCT  OF 
PRESSURE 
AND  VOLUME 

f(?)-X(s)l 

• 

Directions.  —  Read  the  barometer.  No  corrections 
should  be  made,  as  the  mercury  used  in  the  experiment  is 
under  the  same  conditions  as  that  in  the  barometer. 


THE   MECHANICS   OF    SOLIDS  79 

Secure  the  Boyle's  law  tube  in  a  vertical  position  and 
pour  in  enough  mercury  to  fill  the  bend.  Measure  from 
the  table  to  the  top  of  the  meniscus  in  the  short  arm  and 
then  from  the  table  to  the  top  of  the  mercury  in  the  long 
arm.  Now  add  mercury  enough  to  raise  the  level  in  the 
long  arm  10  or  12  cm.  Repeat  the  measurement  of  mer- 
cury cDlumns  in  long  and  short  arms.  Continue  in  this 
way  until  six  or  seven  observations  have  been  recorded  in 
columns  (i)and  (2).  During  your  work  with  this  tube, 
avoid  letting  the  hand  come  in  contact  with  the  confined 
air,  as  any  change  in  its  temperature  would  seriously 
affect  the  final  results.  Why  ? 

Next  measure  the  distance  from  the  table  to  the  top  of 
the  confined  air  column.  Subtract  the  observations  in 
column  (i)  from  this  value  and  record  the  results  in 
column  (3).  The  readings  in  column  (i)  subtracted  from 
the  corresponding  reading  in  column  (2)  should  be  re- 
corded in  column  (4).  Add  the  barometric  reading  to 
each  of  these  values  in  (4)  to  obtain  the  total  pressure  to 
which  the  confined  air  is  subjected,  and  record  these  values 
in  column  (5).  Multiply  the  corresponding  values  in 
columns  (3)  and  (5)  and  record  these  products  in 
column  (6). 

Conclusion.  —  State  Boyle's  law.  What  relation  should 
exist  between  the  quantities  in  column  (6)?  How  does 
this  prove  the  correctness  of  Boyle's  law?  Why  was  it 
necessary  to  add  the  barometric  reading  in  each  case  in 
order  to  obtain  the  total  pressure  on  the  confined  air? 
Would  the  result  have  been  different  if  some  other  gas 
than  air  had  been  placed  in  the  tube  ? 


CHAPTER   VII 

HEAT 
EXPERIMENT  46 

Object.  —  To  test  (a)  the  freezing  point,  (b)  the  boiling 
point,  of  a  mercury  thermometer. 

Apparatus.  —  Thermometer,  a  glass  funnel,  a  ring  stand, 
a  boiler,  a  Bunsen  burner,  a  barometer. 

Data.  — 


OBSERVATIONS 

Reading  of  thermometer  in  melting  ice      .... 
Error  of  thermometer  at  o°  C 

Readin0"  of  thermometer  in  steam 

Corrected  barometer  reading  

Calculated  temperature  of  steam             .          ... 

Error  of  thermometer  at  1  00°  C  

Directions.  —  (a)  Surround  the  bulb  and  stem  of  your 
thermometer  as  far  as  the  zero  mark  with  finely  cracked 
ice,  using  a  funnel  supported  on  a  ring  stand  or  wide 
mouthed  bottle,  to  hold  the  ice.  This  method  allows  the 
water  formed  by  the  melting  of  the  ice  to  be  drained  away, 
—  an  important  point  for  accurate  work. 

80 


HEAT  8 1 

(b)  Pass  the  stem  of  the  thermometer  through  the  cork, 
which  fits  the  top  of  the  boiler,  adjusting  it  until  only  that 
part  of  the  scale  above  the  95  mark  is  visible  above  the 
cork. 

Fill  the  boiler  about  half  full  of  water  and  place  the 
cork  and  the  thermometer  in  position  in  the  boiler.  Care 
must  be  taken  that  the  thermometer  shall  not  touch  either 
the  boiler  or  the  water,  as  these  may  have  a  temperature 
somewhat  higher  than  the  true  boiling  point  or  tempera- 
ture of  the  steam. 

Allow  steam  to  issue  freely  from  one  opening  near  the 
top  of  the  boiler  until  the  mercury  in  the  thermometer 
ceases  to  rise. 

Now  read  the  thermometer  carefully  to  one  tenth  of  one 
degree  and  compare  this  reading  with  the  true  tempera- 
ture of  the  steam  at  the  time  of  the  experiment,  found  as 
follows: 

Calculation  of  the  Boiling  Point  by  the  Barometer. — 
Read  the  barometer  and  obtain  its  corrected  reading  from 
the  formula: 

h  =  n-  -^—(.09 / -  2. 56), 
1000 

where    h  —  true   height   of    barometer   under   standard 

conditions, 

n  —  the  observed  height  of  the  barometer, 
/  =  the  temperature  of  the  barometer  in  degrees 

Fahrenheit. 

% 

Water  boils  at  100°  C.  when  the  barometer  reads 
760  mm.  or  29.92  in.  The  boiling  point  is  raised  .945°  C. 
for  each  additional  inch  of  barometric  pressure  and  is 
depressed  .945°  C.  for  each  inch  below  29.92  in.  In  the 
metric  system  the  change  is  .37°C.  per  centimeter.  From 


82 


PHYSICAL   LABORATORY   GUIDE 


the  true  height  of  the  barometer  and  the  data  just  given, 
calculate  the  true  temperature  of  the  steam  at  the  time  of 
your  experiment.  Compare  the  reading  of  your  thermom- 
eter with  this  temperature.  This  will  give  its  error. 

Conclusion.  —  Why  cannot  the  boiling  point  error  be 
obtained  by  comparing  the  reading  of  the  thermometer  in 
steam  with  100°  C.  ?  Why  is  it  necessary  to  correct  the 
observed  barometer  reading  ? 

NOTE.  —  If  the  laboratory  barometer  has  a  metric  scale,  its  correc- 
tions will  be  found  in  the  tables  in  the  Appendix. 


EXPERIMENT  47 

Object.  —  To  find  how  the  boiling  point  of  water  varies 
with  the  pressure. 

Apparatus.  —  A  boiler  with  a  tightly  fitting  rubber 
stopper  to  hold  a  thermometer,  an  open-end  mercury  ma- 
nometer capable  of  measuring  a  pressure  equal  to  five 
inches  of  mercury  above  atmospheric  pressure,  a  vertical 
scale  for  reading  the  manometer,  a  short  piece  of  rubber 
tube,  a  pinch  cock,  and  a  thermometer. 

Data.  — 


PRESSURE  ABOVE 
THE  ATMOSPHERE 

CORR  ESPONDING 
TEMPERATURE 
OF  THE  STEAM 

INCREASE  IN 
TEMPERATURE  PER  EACH 
ONE  INCH  PRESSURE 

• 

HEAT  83 

Directions.  —  Fill  the  boiler  about  half  full  of  water. 
Pass  the  thermometer  through  the  rubber  stopper  and  put 
it  in  place  in  the  top  of  boiler.  Allow  only  those  divisions 
above  the  95°  point  to  show.  Attach  an  open-end  mer- 
cury manometer  to  the  lower  steam  delivery  tube  and  a 
short  piece  of  rubber  tubing,  provided  with  a  pinch  cock, 
to  the  upper  steam  tube  of  the  boiler. 

Boil  the  water  and  allow  steam  to  issue  from  boiler  with 
pinch  cock  wide  open  until  the  reading  of  the  thermome- 
ter is  constant.  Record  this  temperature  and  then  gradu- 
ally close  the  pinch  cock  until  the  manometer  shows  a 
difference  in  level  of  one  inch  of  the  mercury  columns. 
Manipulate  the  pinch  cock  so  as  to  keep  this  new  pressure 
constant  until  the  temperature  ceases  to  rise.  Record  these 
results.  Now  increase  pressure  to  two  inches  of  mercury. 
Continue  raising  pressure  one  inch  at  a  time  and  recording 
results  until  you  reach  the  limit  of  the  manometer. 

Care  must  be  taken  to  keep  each  pressure  constant  long 
enough  to  allow  thermometer  to  record  the  full  temperature 
corresponding  to  the  steam  pressure. 

Conclusion.  —  What  is  the  average  increase  in  tempera- 
ture for  each  increase  of  pressure  equal  to  a  column  of 
mercury  one  inch  high  ?  How  does  this  compare  with  the 
value  given  in  the  last  experiment  for  the  same  quantity  ? 
If  these  values  are  not  alike,  account  for  the  discrepancy. 

EXPERIMENT  48 

Object — To  find  the  coefficient  of  linear  expansion  of  a 
metal  rod. 

Apparatus.  —  Linear  expansion  apparatus,  a  boiler,  a 
burner,  rubber  tube,  a  thermometer,  a  meter  stick. 


84  PHYSICAL   LABORATORY  GUIDE 

Data.  — 


OBSERVATIONS 

Total  lensfth  of  rod 

Length  of  long  arm  of  pointer 

Length  of  short  arm  of  pointer 

Temperature  of  rod  before  heating    
Temperature  of  rod  after  heating      
Reading  of  pointer  before  heating    
Reading  of  pointer  after  heating  
Actual  expansion  of  the  rod    

Expansion  of  the  rod  per  one  degree     
Linear  coefficient  of  expansion     

Directions.  —  Take  the  apparatus  apart  and  measure  the 
length  of  the  rod  and  the  length  of  the  long  and  short 
arms  of  the  pointer.  Assemble  the  apparatus  again,  con- 
necting the  boiler  with  one  end  of  the  steam  tube  by 
means  of  the  rubber  tubing.  Note  the  temperature  of  the 
air,  and  record  this  as  the  temperature  of  the  rod  when  cold. 
Place  the  thermometer  through  the  cork  in  the  end  of  the 
steam  tube.  The  bulb  should  be  as  near  the  center  of  the 
tube  as  possible,  and  still  allow  you  to  read  it.  Carefully 
adjust  the  apparatus  until  the  rod  rests  against  the  abut- 
ment at  one  end  and  the  short  arm  of  the  lever  at  the  other 
end.  Care  should  be  taken  to  prevent  the  ends  of  the 
steam  tube  from  bearing  against  the  shoulders  of  its  sup- 
ports. There  should  be  a  clearance  of  at  least  one  milli- 
meter at  each  end.  Observe  the  position  of  the  pointer  with 
great  care,  marking  it  if  necessary.  Now  pass  steam  through 
the  apparatus  for  several  minutes  and  again  read  the  position 
of  the  pointer.  Also  record  the  new  temperature  of  the  rod. 

From  this  data  calculate  the  distance  the  pointer  has 
moved,  and  from  this  and  the  ratio  of  the  arms  of  the 


HEAT 


lever  calculate  the  total  expansion  of  the  rod.  Then  cal- 
culate the  expansion  of  the  rod  per  one  degree  change  of 
temperature.  And,  finally,  find  the  increase  in  length,  in 
millimeters,  of  one  millimeter  of  the  rod,  per  one  degree 
change  of  temperature.  This  last  number  is  the  linear 
coefficient  of  expansion  of  brass. 

Conclusion.  —  Define  linear  coefficient  of  expansion  of  a 
substance.  Compare  your  result  with  the  value  given  in 
the  Appendix.  State  the  most  likely  sources  of  error  in 
determining  this  quantity. 

EXPERIMENT  49 

Object.  —  To  study  the  method  of  mixtures  for  measur- 
ing quantity  of  heat. 

Apparatus.  —  A  boiler,  a  burner,  a  calorimeter,  a  ther- 
mometer, a  balance,  a  set  of  weights,  and  a  beaker  or  a 
wide-mouthed  bottle. 

Data.  — 


OBSERVATIONS 

Weight  of  calorimeter                                                  • 

Weight  of  calorimeter  and  hot  water     ..... 
Weight  of  calorimeter,  hot  and  cold  water      .     .     * 

Temperature  of  cold  water      

Temperature  of  hot  water  ... 

Temperature  of  mixture 

Number  of  degrees  cold  water  is  heated     ...» 

Calories  lost  by  hot  water  • 

Calories  lost  by  calorimeter     

Calories  gained  by  cold  water      

Krror      

86  PHYSICAL   LABORATORY   GUIDE 

Directions.  —  Half  fill  the  boiler  with  water  and  heat  it 
to  60°  C.  (approximately).  Adjust  the  balance  and  weigh 
the  empty  calorimeter.  Again  weigh  the  calorimeter, 
this  time  containing  about  150  c.c.  of  the  hot  water.  Put 
about  200  c.c.  of  cold  water  in  the  beaker.  Stir  this  water 
and  then  record  its  temperature.  Now  stir  the  hot  water 
and  record  its  temperature.  Pour  the  cold  water  into  the 
calorimeter.  Stir  with  the  thermometer  for  three  seconds 
and  read  the  temperature.  Stir  and  read  again  until  two 
consecutive  readings  are  obtained  that  are  alike.  Record 
this  as  the  temperature  of  the  mixture.  These  temperatures 
should  be  taken  as  quickly  as  possible  one  after  the  other 
and  the  thermometer  read  to  the  nearest  tenth  of  a  degree 
in  every  case.  Now  weigh  the  mixture. 

Remembering  that  when  a  body  loses  or  gains  heat 
through  a  change  of  temperature,  the  quantity  of  heat 
given  out  or  absorbed  is  always  the  product  of  the  specific 
heat,  the  mass,  and  the  change  of  temperature,  and  also  re- 
membering that  the  total  heat  given  out  equals  the  total 
heat  absorbed  (provided  there  is  no  loss  of  heat  by  radia- 
tion), the  remaining  items  in  the  table  are  easily  calcu- 
lated. 

Conclusion.  —  Distinguish  between  temperature  and  quan- 
tity of  heat.  Define  the  units  by  which  each  is  measured. 
State  the  principles  involved  in  the  method  of  mixtures. 

\  •    • 

EXPERIMENT  60 

Object.  —  To  determine  the  specific  heat  of  a  solid. 

Apparatus.  —  A  boiler  with  a  calorimeter  to  fit,  and  a 
burner,  a  balance,  a  set  of  weights,  two  thermometers, 
another  calorimeter,  and  some  lead  shot  or  copper  filings. 


HEAT 


Data.  — 


OBSERVATIONS 

Weight  of  empty  calorimeter  
Weight  of  calorimeter  and  cold  water    

Wei°"ht  of  calorimeter,  water  and  shot  ..... 

\Vei°"ht  of  water             

^Vei°"ht  of  shot                .           .     .     «     »     •     .     .     • 

Temperature  of  the  cold  water          .               .          . 

Temperature  of  the  hot  water                                  .     •'  • 

Temperature  of  the  mixture                                          .    > 

Number  of  degrees  water  is  heated                            • 

Number  of  degrees  shot  cools                                      » 

Specific  heat  of  shot                                                       .  ' 

Directions.  —  Place  about  300  gm.  of  shot  in  the 
calorimeter.  Heat  this  in  the  boiler,  stirring  from  time  to 
time  with  a  thermometer  to  secure  even  heating.  This 
thermometer  should  be  kept  in  the  shot. 

While  the  shot  is  heating,  adjust  the  balance.  Weigh 
the  empty  calorimeter  and  then  the  same  calorimeter  con- 
taining about  100  c.c.  of  cold  water.  When  the  shot 
attains  a  constant  temperature,  take  the  temperature  of 
the  cold  water.  Quickly  pour  the  shot  into  this  water. 
Stir  thoroughly,  reading  the  thermometer  at  frequent  inter- 
vals. When  the  temperature  remains  constant  for  two  or 
three  of  these  observations,  record  it  as  the  temperature  of 
the  mixture.  Again  weigh  the  calorimeter  and  its  contents. 

Calculate  the  remaining  quantities  in  the  table.  In 
finding  the  specific  heat  of  the  shot,  remember  that  there 
are  two  principles  involved  : 

i.  That  the  heat  lost  by  the  hot  substances  in  cooling 
is  equal  to  the  heat  gained  by  the  cold  substances  in  warm- 
ing. Why  ? 

PHYS.  LAB.  GUIDE — 


88  PHYSICAL   LABORATORY   GUIDE 

2.  That  the  heat  lost  or  gained  by  any  substance 
through  a  change  of  temperature  is  always  equal  to  (spe- 
cific heat)  x  (mass)  x  (change  of  temperature). 

Apply  these  principles,  letting  x  equal  the  specific  heat 
of  shot.  Indicate  the  operations  by  an  algebraic  equation. 
Then  solve  for  x. 

Conclusion.  —  Define  specific  heat  of  a  substance.  Com- 
pare your  result  with  the  known  value.  What  in  your 
opinion  are  the  most  probable  sources  of  error  ?  State  the 
two  principles  given  above. 

NOTE.  —  Obtain  specific  heat  of  calorimeter  from  your  instructor. 
The  calorimeter  is  one  of  the  bodies  warmed. 

EXPERIMENT   51 
Object.  —  To  determine  the  latent  heat  of  fusion  of  ice. 

Apparatus.  —  A  boiler,  a  burner,  a  calorimeter,  a  ther- 
mometer, a  balance,  a  set  of  weights,  a  blotter,  and  ice  in 
lumps  about  the  size  of  hickory  nuts. 

Data.  — 


OBSERVATIONS 

Weight  of  empty  calorimeter  

Weight  of  calorimeter  and  hot  water     
Weight  of  calorimeter,  water  and  melted  ice  . 
\Veiaht  of  hot  water                                           .     .     . 

^^eight  of  ice  added 

Temperature  of  water  before  adding  ice     ...     . 
Temperature  of  the  mixture 

Number  of  degrees  hot  water  cools        .     .     .     .    ••'  • 

Number  of  degrees  melted  ice  is  warmed   .     .     .     , 
Latent  heat  of  fusion  of  ice      .          ...... 

HEAT  89 

Directions.  —  Fill  the  boiler  about  half  full  of  water  and 
heat  it  to  60°  approximately.  Weigh  the  calorimeter 
empty  and  also  when  it  contains  about  150  c.c.  of  the  hot 
water.  Prepare  enough  lumps  of  ice  the  size  of  a  hickory 
nut  to  weight  approximately  40  gm.  Bend  a  blotter 
lengthwise  through  the  center  to  form  a  V-shaped  trough. 
Place  the  ice  on  this  and  dry  each  lump  just  as  you  drop 
it  into  the  hot  water. 

Special  care  should  be  exercised  at  this  point,  as 
adding  water  with  the  ice  would  cause  a  serious  error. 
Why? 

The  temperature  of  the  hot  water  should  be  taken  just 
before  adding  the  ice  and  the  temperature  of  the  mixture 
just  as  soon  as  the  ice  is  all  melted  and  the  water  thor- 
oughly stirred.  Weigh  the  mixture  to  find  the  exact 
weight  of  ice  added. 

Apply  the  following  principles  to  calculate  the  latent 
heat  of  fusion  of  ice  : 

1.  The  heat  lost  by  the  hot    substances  in  cooling  is 
equal  to  the  heat  gained  by  the  cold  substances  in  warming. 
Why? 

2.  The  heat  lost  or  gained  by  any  substance  through  a 
change   of   temperature   equals   (specific  heat)  X  (mass)  x 
(change  of  temperature). 

3.  The  heat  lost  or  gained  by  any  substance  through  a 
change  of  form  equals  (latent  heat)  X  (mass). 

Notice  (a)  that  both  the  hot  water  and  the  calorimeter 
lose  heat  by  cooling,  (b)  that  the  ice  takes  in  heat  first  in 
melting,  second  to  heat  the  resulting  water  to  the  temper- 
ature of  the  mixture. 

Conclusion.  —  Define  latent  heat  of  fusion.  Compare 
your  result  with  the  known  value.  What  are  the  most 


90  PHYSICAL   LABORATORY   GUIDE 

probable  sources  of  error  ?     State  the  principles  involved 
in  this  experiment. 

NOTE. — Obtain  specific  heat  of  calorimeter  from  your  instructor. 
The  calorimeter  is  one  of  the  bodies  cooled. 


EXPERIMENT  62 

Object.  —  To  determine  the  latent  heat  of  vaporization 
of  steam. 

Apparatus.  —  A  boiler  and  cover,  a  burner,  a  calorimeter, 
a  thermometer,  a  balance,  a  set  of  weights,  and  a  steam 
trap. 

Data.  — 


OBSERVATIONS 


Weight  of  empty  calorimeter 

Weight  of  calorimeter  and  cold  water 

Weight  of  calorimeter,  water  and  condensed  steam. 

Weight  of  cold  water 

Weight  of  steam  added 

Temperature  of  water  before  adding  steam 

Temperature  of  the  mixture 

Number  of  degrees  water  is  heated 

Number  of  degrees  condensed  steam  cools     .     .     . 
Latent  heat  of  vaporization  of  steam 


Directions.  —  Weigh  the  calorimeter  empty  and  when  it 
contains  200  gm.  of  cold  water.  Take  the  temperature 
of  this  water  and  immediately  pass  steam  into  it  from 
the  boiler.  The  delivery  tube  should  dip  about  2  cm. 
under  the  water,  and  the  steam  trap  should  be  3  or  4  cm. 
above  the  water.  A  paper  pad  or  other  non-conducting 


HEAT  91 

substance  should  be  placed  between  the  boiler  and  the 
calorimeter.  This  will  prevent  the  absorption  of  heat  by 
radiation. 

Continue  the  heating  of  the  water  by  the  steam, 
stirring  the  mixture  continually  until  the  temperature 
reaches  about  40°  C.  Remove  the  calorimeter  quickly 
from  the  steam  supply.  Stir  the  mixture  thoroughly,  and 
record  its  exact  temperature.  Weigh  the  calorimeter  and 
its  contents  and  calculate  the  weights  of  water  and  steam 
used. 

To  find  the  latent  heat  of  steam  apply  the  three  prin- 
ciples stated  in  the  last  experiment,  remembering  (a)  that 
the  steam  loses  heat  in  condensing  and  also  by  the  cooling 
of  the  water  it  forms,  (b)  that  both  the  cold  water  and  the 
calorimeter  are  raised  in  temperature  and  therefore  absorb 
the  heat  given  out  by  the  steam. 

Conclusion.  —  Define  latent  heat  of  vaporization.  Com- 
pare your  result  with  the  known  value.  State  the  most 
probable  sources  of  error. 

NOTE.  —  Obtain  temperature  of  steam  from  the  barometer.  See 
Experiment  43  for  directions  necessary  to  make  this  calculation. 

s^ 

EXPERIMENT  63 

Object. — To  determine  the  dew  point  and  per  cent  of 
humidity  of  the  air  in  the  laboratory. 

Apparatus.  —  A  polished  calorimeter,  a  thermometer, 
finely  cracked  ice,  either  sal  ammoniac  or  common  salt, 
and  a  teaspoon.  A  sling  psychrometer  (desirable  but  not 
essential).  This  instrument  depends  upon  the  change  in 
rate  of  evaporation  with  a  change  in  the  humidity. 


92  PHYSICAL   LABORATORY   GUIDE 

Data.  — 


OBSERVATIONS 

Temperature  of  the  laboratory 

Temperature  when  the  dew  first  appears    .... 
Temperature  when  the  dew  begins  to  disappear  .     . 
Water  vapor  in  one  kilogram  of  air  to-day      .     .     . 
Water  vapor  to  saturate  one  kilogram  of  air  to-day. 
Calculated  dew  point     

Calculated  per  cent  of  relative  humidity     .... 

Directions.  —  Pour  cold  water  into  the  calorimeter  to  a 
depth  of  about  3  cm.  Stir  the  water  with  the  thermome- 
ter and  note  its  temperature.  Add  the  cracked  ice,  very 
little  at  a  time,  with  a  teaspoon,  stirring  constantly.  The 
temperature  should  drop  about  one  half  of  one  degree  each 
time  the  ice  is  added.  Continue  in  this  way  until  dew 
begins  to  form  on  the  outside  of  the  calorimeter.  Note 
carefully  the  temperature  at  which  this  occurs.  Allow 
the  calorimeter  to  warm  gradually,  stirring  from  time  to 
time.  Note  the  temperature  when  the  dew  begins  to  dis- 
appear. The  average  of  these  temperatures  is  the  dew 
point.  If  the  dew  point  is  below  o°  C.,  it  will  be  necessary 
to  add  sal  ammoniac  or  salt  with  the  ice.  Avoid  letting 
moisture  from  the  hand  or  breath  come  in  contact  with  the 
calorimeter. 

From  the  table  in  the  Appendix  find  the  weight  of  water 
vapor  necessary  to  saturate  one  kilogram  of  air  at  the  dew 
point.  This  will  be  the  actual  weight  of  water  vapor  in  one 
kilogram  of  the  air  in  the  laboratory  at  the  time  of  the 
experiment.  From  the  same  table  find  the  weight  of 
water  vapor  necessary  to  saturate  the  same  weight  of 
air  at  the  temperature  of  the  laboratory.  The  ratio  be- 


HEAT  93 

tween  these  weights  just  found  reduced  to  decimal  form 
will  give  the  per  cent  of  relative  humidity  at  the  time 
of  the  experiment. 

Conclusion.  —  Define  dew  point  and  per  cent  of  humidity. 
Would  the  dew  point  be  the  same  if  you  performed  the 
experiment  outdoors  ?  Would  the  per  cent  of  humidity 
be  the  same  ?  Why  ?  What  two  things  cause  the  per 
cent  of  humidity  to  change  from  time  to  time  ?  Why  does 
a  high  humidity  make  a  hot  summer's  day  so  much  more 
uncomfortable  ?  Why  will  ice  and  salt  lower  the  tempera- 
ture of  the  water  in  the  calorimeter  below  o°  C.,  while  ice 
alone  will  not  ? 

NOTE.  —  If  a  sling  psychrometer  is  available,  obtain  the  readings  of 
its  wet  and  dry-bulb  thermometers  after  whirling  it  about  gently  for  a 
few  moments. 

From  the  depression  of  the  mercury  in  the  wet-bulb  thermometer  and 
the  meteorological  tables  given  in  Chapter  XI  find  the  dew  point  and 
per  cent  of  humidity. 

Compare  these  values  with  those  obtained  by  the  calorimeter  method. 


CHAPTER   VIII 

LIGHT 
EXPERIMENT  54 

Object. — To  measure  the  candle  power  of  a  gas  flame 
or  incandescent  lamp  by  means  of  a  Rumford  photometer. 

Apparatus.  —  A  large  candle,  a  gas  flame  or  an  incan- 
descent lamp,  an  opaque  rod  and  support,  a  piece  of  red 
glass,  a  meter  stick,  a  white  cardboard  screen  and  support. 

Directions.  —  Set  up  the  vertical  screen  and  place  the 
opaque  rod  in  front  of  it  and  about  3  cm.  away.  Arrange 
the  candle  and  light  to  be  measured  about  50  cm.  from 
the  screen  and  in  such  positions  that  the  two  shadows  cast 
by  the  rod  are  close  together. 

Notice  that  the  shadows  are  of  unequal  intensity.  Move 
the  lights  toward  or  away  from  the  screen  until  the 
shadows  are  equally  dark.  View  them  through  a  piece 
of  red  glass.  This  will  do  away  with  difference  in  color 
and  make  the  comparison  easier. 

Now  measure  the  distance  from  the  center  of  each  light 
to  the  shadow  which  it  illuminates.  Remembering  that 
the  candle  powers  of  lights  vary  directly  as  the  squares 
of  their  distances  from  a  screen  which  they  illuminate 
equally,  calculate  the  candle  power  of  the  gas  flame  or 
the  incandescent  lamp. 

94 


LIGHT  95 

Make  at  least  three  trials,  using  different  distances. 
Record  the  measurements  and  calculated  results  in  tabular 
form.  The  arrangement  of  this  table  is  left  to  the  pupil. 
Care  should  be  taken  to  keep  the  candle  burning  with  a 
normal  flame  without  smoking.  This  is  accomplished  by 
gradually  cutting  the  wick  shorter  a  very  little  at  a  time. 

Conclusion.  —  Compare  the  law  given  for  candle  power 
under  the  conditions  of  this  experiment  with  the  law  of 
inverse  squares  for  the  intensity  of  illumination. 

EXPERIMENT  56 

Object.  —  To  measure  the  candle  power  of  a  gas  flame 
or  an  incandescent  lamp  by  means  of  a  Bunsen  pho- 
tometer. 

Apparatus.  —  A  large  candle,  a  gas  flame  or  an  incan- 
descent lamp,  a  Bunsen  photometer,  and  a  meter  stick. 

Directions.  —  Set  up  the  photometer  in  a  darkened  room 
with  the  candle  on  one  side  of  the  screen  and  the  light  to 
be  measured  on  the  other.  Adjust  the  position  of  the 
screen,  moving  it  toward  or  away  from  the  candle  until 
its  translucent  and  opaque  surfaces  appear  equally  illu- 
minated. When  this  position  is  correctly  found,  measure 
the  distances  from  the  candle  and  the  lamp  to  the  screen. 

Remembering  that  the  candle  powers  of  lights  vary 
directly  as  the  squares  of  their  distances  from  a  screen 
which  they  illuminate  equally,  calculate  the  candle  power 
of  the  gas  flame  or  the  incandescent  lamp. 

Make  at  least  three  trials.  Record  the  measurements 
and  calculated  results  in  tabular  form.  The  arrangement 
of  this  table  is  left  to  the  pupil. 


96  PHYSICAL   LABORATORY   GUIDE 

Care  should  be  taken  to  keep  the  candle  burning  with 
a  normal  flame  without  smoking.  This  is  accomplished 
by  cutting  the  wick  off  a  very  little  at  a  time. 

Explanation.  —  When  the  apparatus  is  correctly  ad- 
justed, view  the  screen  from  the  candle  side  and  note  that 
the  light  which  reaches  your  eye  from  the  opaque  portion 
of  the  screen  is  reflected  light  from  the  candle,  whereas 
the  light  which  comes  to  your  eye  from  the  translucent 
spot  is  direct  light  from  the  lamp  on  the  other  side  of  the 
screen.  Therefore  when  all  parts  of  the  screen  are 
equally  illuminated,  the  lamp  and  the  candle  are  giving  the 
same  intensity  of  illumination  at  their  respective  distances 
from  the  screen.  Hence  their  candle  powers  are  directly 
proportional  to  the  squares  of  their  distances  from  the 
screen.  In  some  forms  of  Bunsen  photometer  mirrors  are 
provided  for  viewing  both  sides  of  the  translucent  spot  at 
once.  This  is  a  decided  advantage. 

Conclusion.  —  State  some  of  the  difficulties  connected 
with  accurate  photometric  work. 

A  standard  candle  should  burn  120  gr.  of  the  wax 
per  hour.  In  the  light  of  this  statement,  suggest  how,  if 
time  permitted,  you  might  increase  the  accuracy  of  your 
work  still  further. 

State  the  law  of  intensity  of  illumination  and  the  law  of 
candle  powers.  Compare  them. 

EXPERIMENT  56 

Object.  —  To  find  the  position  and  size  of  an  image  as 
seen  in  a  plane  mirror. 

Apparatus.  —  A  plane  mirror,  supporting  block,  and 
rubber  band,  a  small  block  with  a  vertical  black  mark,  a 


LIGHT  97 

pair  of   drawing   compasses,  and  a  sheet  of  white  paper 
about  12  x  20  in. 

Directions.  —  Draw  a  straight  line  on  the  sheet  of  paper 
connecting  the  middle  points  of  the  long  sides.  Attach 
the  mirror  to  the  block  with  a  rubber  band.  Place  the 
reflecting  surface  of  the  mirror  over  the  line  just  drawn, 
The  middle  point  of  the  mirror  should  bisect  this  line,  and 
the  surface  of  the  mirror  should  be  exactly  vertical. 
Draw  an  equilateral  triangle  in  front  of  the  mirror  with 
its  base  parallel  to  the  short  edge  of  the  paper  and  about 
3  cm.  from  this  edge.  Use  the  compasses  for  this  purpose 
and  make  each  edge  8  cm.  long.  Number  the  vertices 
of  this  triangle  I,  2,  and  3. 

Place  the  small  block  so  that  the  foot  of  the  vertical 
mark  coincides  exactly  with  vertex  I  of  the  triangle. 
Place  the  ruler  in  such  a  position  that  a  line  drawn  along 
its  edge,  if  produced,  would  appear  to  pass  through  the 
image  of  vertex  I.  From  the  opposite  side  of  the  paper 
sight  another  line  to  pass  through  the  same  point.  Make 
the  angle  between  these  lines  as  great  as  possible. 
Number  each  of  these  lines  I.  Next  place  the  vertical 
line  over  vertex  2  and  locate  its  image.  Find  the  image 
of  vertex  3  in  the  same  manner.  Remove  the  mirror  and 
produce  the  lines  just  sighted  until  lines  (i)  (i),  (2)  (2), 
and  (3)  (3)  intersect.  Connect  these  points  by  dotted 
lines  to  form  the  image  of  the  triangle.  Number  these 
vertices  ir,  2',  and  3'.  Now  draw  dotted  lines  connecting 
points  i  and  i',  2  and  2',  also  3  and  3'. 

Conclusion. — What  kind  of  an  image  is  formed  by  a 
plane  mirror  ?  How  do  you  know  this  ?  Is  this  image 
erect  or  inverted  or  reversed  ?  How  does  its  size  compare 


98  PHYSICAL   LABORATORY   GUIDE 

with  that  of  the  object  ?  Compare  the  distance  of  points 
I  and  i',  2  and  2',  etc.,  from  the  mirror.  What  angles  do 
lines  i-i',  2-2',  and  3-3'  make  with  the  reflecting  surface 
of  the  mirror  ? 

NOTE.  —  Great  care  should  be  exercised  in  making  the  drawing  in 
this  experiment,  and  also  in  a  number  of  the  experiments  on  Light,  as 
any  inaccuracy  will  give  misleading  results. 

EXPERIMENT  57 

Object.  —  To  determine  the  index  of  refraction  from  air 
to  glass. 

Apparatus.  —  A  piece  of  plate  glass,  a  straightedge,  a 
scale,  pins,  a  sheet  of  notebook  paper,  and  drawing  com- 
passes. 

Directions.  —  Through  the  center  of  the  sheet  of  paper 
draw  a  straight  line  parallel  to  one  of  its  shorter  edges. 
Place  the  piece  of  glass  on  the  side  of  this  line  farthest 
from  you  so  that  one  of  its  polished  edges  coincides  with 
the  line.  Stick  a  pin  against  the  glass  perpendicular  to 
the  paper  and  at  its  center.  If  the  glass  has  been  prop- 
erly placed,  this  pin  will  now  be  at  a  point  distant  one  third 
of  the  length  of  the  glass  plate  from  the  end  of  the  plate. 
On  the  opposite  side  of  the  glass  place  another  pin  distant 
one  third  of  the  length  of  the  glass  plate  from  the  other 
end  of  the  plate.  Now  sight  with  the  straightedge  until  a 
line  drawn  along  it  would  pass  through  the  nearest  pin 
and  appear  to  pass  through  the  image  of  the  opposite  pin 
as  seen  through  the  glass.  Draw  this  line  and  then 
remove  both  pins  and  the  glass.  Draw  a  second  line 
through  these  two  pinholes  to  meet  the  first.  The  first 
line  is  the  path  of  a  ray  in  the  air  along  which  the  observer 
looks  ;  the  second,  its  path  through  the  glass.  Why  ? 


LIGHT  99 

Great  care  should  be  exercised  in  sighting  this  ray,  as 
any  inaccuracy  here  will  seriously  affect  the  final  result. 

Through  the  point  where  the  ray  enters  the  glass  draw 
a  perpendicular  to  this  edge  of  the  glass.  Next,  lay  off 
equal  distances  from  this  point  on  the  rays  in  the  air  and 
in  the  glass.  From  these  points  draw  normals  to  the  per- 
pendicular. Measure  the  lengths  of  these  normals  accu- 
rately. The  ratio  of  their  lengths  will  be  the  required 
index  of  refraction. 

In  laying  off  the  equal  distances  referred  to  above,  it  is 
well  to  make  them  as  great  as  is  practicable.  Why  ? 

Conclusion.  —  The  pin  seen  over  the  glass  and  the  same 
pin  seen  through  the  glass  do  not  coincide.  Explain  this. 
Can  you  find  any  position  from  which  you  could  view  this 
pin  and  have  the  pin  seen  above  and  through  the  glass 
coincide  ?  Why  ?  Does  the  distance  you  choose  to  lay 
off  on  the  two  rays  affect  the  value  of  the  index  ?  Try  it. 
Does  the  angle  of  incidence  chosen  affect  the  index  value? 
Try  an  angle  different  from  the  one  first  drawn  and  com- 
pare the  results.  This  point  should  be  settled  carefully,  as 
it  is  of  great  importance.  What  do  you  conclude  would 
affect  the  value  of  the  index  of  refraction  ?  Compare 
your  results  with  the  correct  value  given  in  the  table  (see 
Chap.  XI).  Is  the  value  you  have  found  the  index  from 
air  to  glass  or  from  glass  to  air  ?  Find  the  value  for  the 
other. 

EXPERIMENT  68 

Object.  —  To  find  the  index  of  refraction  from  air  to 
water. 

Apparatus.  —  A  glass  jar,  a  metal  bridge  to  fit  the  jar,  a 
metal  index  to  slide  upon  the  edge  of  the  jar,  a  3O-cm. 
rule,  a  pair  of  drawing  compasses. 


100  PHYSICAL   LABORATORY   GUIDE 

Directions.  —  Put  the  bridge  in  position.  Care  should 
be  taken  to  have  the  bridge  perpendicular  to  the  surface 
of  the  water,  which  should  come  as  close  as  possible  to  its 
lower  edge  without  touching  it. 

Now  looking  along  the  diameter  of  the  jar,  which  is 
perpendicular  to  the  plane  of  the  bridge,  sight  the  appara- 
tus until  the  inner  edge  of  the  jar,  the  lower  edge  of  the 
bridge,  and  the  point  of  the  index  appear  to  be  in  line. 
Are  they  ?  It  will  be  necessary  to  raise  or  lower  the  index 
until  its  correct  position  is  found. 

Make  a  drawing  of  the  jar  (full  size).  Use  the  inside 
diameter  of  the  jar  and  carefully  locate  the  position  of  the 
bridge,  index,  and  water  surface,  etc.  This  is  best  done  by 
talking  all  vertical  measurements  from  the  table  up.  Draw 
a  line  from  this  point  of  the  index  to  the  lower  surface  of 
the  bridge  and  another  from  this  last  point  to  the  edge  of 
the  jar  along  which  you  sighted.  These  lines  represent  the 
path  of  the  ray,  along  which  you  looked,  in  the  water 
and  in  the  air,  respectively.  Are  the  three  points  on  the 
same  straight  line  ?  Why  ? 

Draw  a  normal  to  the  surface  of  the  water  at  the  point 
where  the  ray  enters  it.  Lay  off  from  this  point  equal 
distances  on  the  rays  in  the  water  and  in  the  air. 
Make  these  distances  as  large  as  practicable.  From  the 
points  thus  found,  draw  perpendiculars  to  the  normal. 
These  lines  are  the  sines  of  the  angles  of  incidence  and 
refraction.  Measure  their  lengths  accurately.  The  ratio 
of  these  lengths  gives  the  index  of  refraction. 

Conclusion.  —  Define  incident  and  refracted  ray.  Sup- 
pose you  had  arranged  the  apparatus  so  that  the  angle  of 
incidence  was  different ;  would  this  have  changed  the  value 
of  angle  of  refraction  ?  Would  it  have  changed  the  value 


LIGHT    :          ,i>a  tijj  ioi 

of  their  sines  ?  Would  it  give  a  different  value  for  the 
index  of  refraction  ?  Compare  your  result  with  the  known 
value. 

EXPERIMENT   59 

Object.  —  To  find  the  focal  length  of  a  double  convex 
lens.  Two  methods  :  (a)  by  throwing  the  image  of  a  dis- 
tant object  on  a  screen ;  (£)  by  the  method  of  parallax. 

Apparatus. — A  meter  stick,  a  screen,  a  double  convex 
lens,  a  pin  mounted  on  a  sliding  block,  a  3O-cm.  scale. 

Directions.  —  (a)  Darken  the  laboratory  by  drawing  the 
shades.  Have  one  window  open  from  the  bottom.  Take 
your  position  on  the  side  of  the  room  opposite  this  open 
window.  Place  the  lens  and  screen  upon  the  meter  stick, 
mounted  in  such  a  way  that  either  will  slide  on  the  stick. 
Focus  the  lens  until  a  sharp  image  of  some  distant  object 
out  of  doors  is  formed  upon  the  screen.  A  tall  chimney, 
flagstaff,  or  steeple  will  answer  well.  The  object  should 
be  at  least  one  eighth  of  a  mile  away.  Why  ?  What  rays 
intersect  only  at  the  principal  focus  of  a  double  convex 
lens  ? 

Now  measure  the  distance  from  the  optical  center  of  the 
lens  to  the  center  of  the  image.  This  will  give  the  focal 
length  of  the  lens.  Why?  Make  several  trials,  using 
different  objects  and  resetting  the  lens  each  time. 

(b)  Replace  the  screen  with  the  pin  mounted  vertically 
on  the  sliding  block.  Raise  all  the  shades.  Rest  the 
meter  stick  on  any  convenient  support.  Look  through 
the  lens  at  one  of  the  distant  objects  used  in  part  (a).  A 
real,  inverted  image  will  be  seen.  Place  the  pin  where 
you  think  this  real  image  is.  Now,  while  looking  at  this 
image  and  the  pin,  move  your  head  from  side  to  side  and 


102  PHYSICAL  -LABORATORY   GUIDE 

note  whether  they  remain  the  same  distance  apart.  They 
should.  If  they  do  not,  try  other  positions  until  you  find 
the  correct  one.  The  distance  from  the  pin  to  the  optical 
center  of  the  lens  is  its  focal  length.  Why  ?  Try  the 
same  principle,  using  two  pencils  held  upright.  Note 
how  the  distance  between  them  seems  to  vary  except  when 
they  are  side  by  side. 

Record  the  results  of  both  parts  in  one  table.  Average 
the  trials  made  with  each  method.  Average  these  results, 
if  they  are  not  alike,  and  take  this  as  the  true  focal  length 
of  the  lens. 

Conclusion.  —  Which  method  is  more  accurate  in  your 
opinion  ?  Why  ?  What  is  meant  by  the  term  parallax  ? 
Use  the  dictionary  if  necessary.  Define  focal  length  of  a 
lens.  Also  define  optical  center  of  a  lens. 


EXPERIMENT  60 

Object.  —  To  test  the  formula  —  =  —  +  -^-.  for  a  double 

F     Do     Dt 

convex  lens  :  a  study  of  conjugate  foci. 

Apparatus.  —  A  candle,  a  double  convex  lens  and  holder, 
a  paper  screen  and  support,  and  a  meter  stick. 

Directions.  —  With  the  room  darkened  and  the  lens 
between  the  candle  and  the  screen,  adjust  the  apparatus 
until  a  clear  image  of  the  candle  is  formed.  In  focusing 
the  image,  attention  should  be  directed  to  the  candle  wick 
or  some  other  detail  in  order  to  obtain  the  best  results. 
If  the  room  is  not  very  dark,  the  screen  should  be  so 
placed  that  direct  light  from  the  windows  cannot  strike  it. 

Now  measure  the  distances  from  the  optical  center  of  the 


LIGHT  103 

lens  to  the  image  on  the  screen  (image  distance,  Di)  and 
the  distances  to  the  candle  (object  distance,  Do).  At  least 
three  trials  should  be  made,  using  a  different  object  dis- 
tance each  time. 

Substitute  these  values  in  the  lens  formula  —  =  — *H , 

F     Do     Dz 

and  solve  for  F  the  focal  length  of  the  lens.  Average  the 
values  thus  found  and  compare  the  result  obtained  with 
the  known  focal  length  of  the  lens  as  determined  in  Ex- 
periment 56.  Record  the  data  in  tabular  form. 

Conclusion.  —  Define  conjugate  foci.  Are  these  foci 
interchangeable  ?  Test  this  point  first  by  focusing  image 
of  candle  on  the  screen,  marking  positions  of  candle  and 
screen  in  some  way,  and  second  by  changing  these  objects 
about.  Is  the  image  formed  still  in  good  focus  ?  Suggest 
some  practical  optical  problems  for  whose  solution  this  lens 
formula  would  be  valuable. 

EXPERIMENT  61 

Object.  —  To  study  the  spectroscope  and  the  three  kinds 
of  spectra. 

Apparatus.  —  A  spectroscope,  a  spectrum  chart,  a  Bun- 
sen  burner,  a  small  platinum  wire  mounted,  solutions  of 
salts  of  the  alkaline  earth  metals,  pieces  of  red,  green,  and 
blue  glass,  solution  (dilute)  of  chlorophyll  in  a  bottle  with 
flat  sides  (soda  mint  bottle). 

Directions.  I.  —  Remove  the  cover  from  the  circular 
box  at  the  top  'of  the  vertical  support.  Note  carefully  the 
position  of  the  prism.  Unscrew  the  telescope  from  the 
support  and  note  the  number  and  position  of  its  lenses. 

PHYS.  LAB.  GUIDE  —  8 


104  PHYSICAL  LABORATORY   GUIDE 

Look  through  it  at  objects  across  the  street.  Remove  the 
draw  tube  from  the  collimator  and  note  position  of  adjus- 
table slit  and  lens.  Now  make  a  careful  diagram  of  the 
instrument,  looking  down  from  above,  showing  position  of 
prism, -telescope,  collimator  tubes,  and  all  lenses.  Explain 
the  use  of  the  various  parts. 

II.  With    the    spectroscope    properly   assembled,   now 
point  the  collimator  toward  the  sky  and  adjust  slit  and 
telescope  until  the  more  prominent  Fraunhofer  lines  are 
clearly  seen.     Compare  these  with  the  picture  of  the  solar 
spectrum  given,  and  decide  which  lines  you  have  seen. 
What  is  the  name  of  this  class  of  spectra,  and  what  other 
sources  of  light  would  give  the  same  result  ? 

Darken  the  room  and  adjust  the  spectroscope  again, 
using  a  luminous  gas  flame  as  the  source  of  light.  Does 
this  spectrum  show  any  dark  lines  ?  Name  this  class  of 
spectra.  Under  what  conditions  is  this  kind  of  spectrum 
always  obtained  ? 

Use  the  non-luminous  Bunsen  flame  and  dip  a  platinum 
wire  into  one  of  the  solutions  given.  Compare  this  spec- 
trum carefully  with  the  chart  given,  and  decide  what  mate- 
rial is  in  the  solution.  Test  the  other  solutions  in  the  same 
way.  Name  this  third  class  of  spectra. 

III.  Using  the  luminous  gas  flame  as  a  source  of  light, 
hold  the   different   colored   pieces   of   glass   successively 
between  the  source  of  light  and  the  slit.     Account  for  the 
results.     Hold  the  bottle  of  chlorophyll  solution  between 
the  light  and  the  slit,  and  note  the  result. 

Conclusion.  —  Name  and  explain  the  practical  applica- 
tions of  the  spectroscope  based  on  the  experiments  you 
have  just  performed. 


CHAPTER    IX 

SOUND 
EXPERIMENT  62 

Object.  —  To  plot  several  wave  motions  on  section  paper 
and  to  find  the  resultant  wave  in  each  case. 

Apparatus.  —  Section  paper  ruled  to  inches,  half  inches, 
and  tenths  of  inches,  or  section  paper  ruled  to  centimeters 
and  millimeters,  a  pair  of  drawing  compasses,  and  a  blue 
pencil. 

NOTE.  —  If  metric  paper  is  provided,  use  centimeters  to  replace  half 
inches. 

Directions.  —  CASE  i.  Draw  a  straight  line  lengthwise 
through  the  middle  of  a  sheet  of  section  paper.  This  line 
should  coincide  with  one  of  the  half-inch  (centimeter)  ruled 
lines  on  the  paper.  Near  the  left-hand  end  of  this  line 
draw  a  circle  of  i^-inch  radius.  The  center  of  this  circle 
should  be  on  the  line  just  drawn  and  should  coincide  with 
an  intersection  of  the  half-inch  lines.  Divide  this  circle 
into  twelve  equal  parts.  Do  this  with  the  compasses, 
using  points  on  the  circumference  90°  apart  as  centers 
and  drawing  arcs  to  intersect  the  circle.  The  radius  used 
is  the  radius  of  the  circle. 

Now  locate  the  successive  positions  of  the  vibrating  par- 
ticles causing  the  wave  motion,  as  follows :  Suppose  the 
first  particle  to  be  on  the  first  vertical  half-inch  line  to  the 

I05 


106  PHYSICAL   LABORATORY   GUIDE 

right  of  the  circle  and  to  coincide  with  the  horizontal  axis, 
the  second  particle  to  be  on  the  second  half-inch  vertical 
line  and  above  the  axis.  Its  position  may  be  found  by 
projecting  the  second  division  on  the  circle  upon  this  ver- 
tical line.  Continue  in  this  manner,  advancing  one  divi- 
sion on  the  circle  and  one  half-inch  along  the  axis  to  the 
right  until  the  points  are  plotted  for  one  complete  wave 
consisting  of  a  crest  and  trough.  Draw  a  solid  pencil  line 
through  these  points  to  complete  the  wave. 

Beginning  at  the  same  points  on  axis  and  curve,  but 
advancing  along  the  circle  in  the  opposite  direction,  locate 
the  points  for  another  complete  wave.  Draw  a  dotted 
pencil  line  through  these  points. 

Counting  distance  above  the  horizontal  axis  plus-dis- 
placement, and  distance  below,  minus-displacement,  locate 
the  points  of  the  wave  motion  resulting  from  the  combina- 
tion of  the  two  waves  just  drawn.  Draw  a  blue  line 
through  these  points. 

What  is  the  amplitude  of  these  waves  ?  What  is  their 
length  ?  Are  they  in  like  or  opposite  phase  ?  What  phe- 
nomenon in  sound  does  this  drawing  illustrate  ?  Mark 
it  so. 

CASE  2.  In  like  manner  make  another  drawing  on  a 
separate  sheet  of  paper  showing  these  waves  in  like  phase. 
Find  the  resultant  wave.  What  phenomenon  does  this 
drawing  illustrate  ?  Mark  it  so. 

CASE  3.  On  a  third  sheet  of  paper  draw  two  waves  — 
the  first  to  be  precisely  like  those  drawn  in  Cases  I  and  2, 
and  the  second  to  have  one  half  the  wave  length  an'd  two 
thirds  the  amplitude  of  the  first.  Find  the  resultant 
curve.  This  drawing  shows  a  fundamental  tone  and  its 
first  harmonic  sounded  together.  What  musical  interval 
exists  between  the  notes  ?  Why  ? 


SOUND  107 

Conclusion.  —  How  is  a  simple  harmonic  motion  plotted  ? 
What  kind  of  motion  does  a  particle  vibrating  in  a  medium 
transmitting  sound  have?  Of  what  kind  is  the  onward 
motion  of  the  wave  itself  ? 

EXPERIMENT  63 

Object.  —  To  find  the  number  of  vibrations  made  in  one 
second  by  a  tuning  fork. 

Apparatus.  —  A  tuning  fork  apparatus  (consisting  of  a 
large  heavy  fork,  and  a  quarter-seconds  pendulum  with 
needle  point,  several  pieces  of  glass,  a  carrier  and  carrier 
track),  gum  camphor,  matches,  bristles  and  wax  for  attach- 
ing them  to  a  prong  of  the  fork,  a  bass  viol  bow,  a  watch, 
and  crucible  tongs  or  a  pair  of  tweezers. 

Data.  — 


OBSERVATIONS 

Vibrations  of  fork  per  one  pendulum  vibration    .     . 
Vibrations  of  fork  in  one  second  (calculated)       .  '  ,  -. 
Vibrations  of  fork  in  one  second  (stamped)    .     .    ;.    ' 

Directions.  —  By  means  of  a  piece  of  burning  camphor 
held  in  the  tongs,  smoke  several  of  the  glass  slides  on  one 
side.  The  film  of  smoke  should  be  as  light  as  possible  and 
still  completely  cover  the  glass. 

Attach  a  bristle  to  one  prong  of  the  fork.  This  is  best 
done  by  warming  one  end  of  the  fork  in  a  flame  until  it 
will  just  melt  the  wax.  Attach  the  bristle,  using  as  little 
wax  as  possible.  Why  ? 

Next  set  up  the  apparatus  and  adjust  the  stylus  on  the 
pendulum  and  the  bristle  o'n  the  fork  until  they  are  as 


108  PHYSICAL  LABORATORY   GUIDE 

close  together  as  possible  without  touching.  Each  should 
just  graze  the  smoked  glass. 

Set  the  fork  and  pendulum  in  vibration  at  the  same 
time  and  quickly  draw  the  glass  plate  along  the  track 
under  the  fork.  If  the  work  is  carefully  timed,  you  will 
now  have  a  record  of  two  or  three  swings  of  the  pendu- 
lum together  with  the  more  rapid  vibration  of  the  fork 
traced  on  the  glass.  Some  patience  and  practice  are 
necessary  to  obtain  a  good  record. 

When  two  or  more  clear  records  are  obtained,  count  the 
number  of  vibrations  of  the  fork  to  each  pendulum  vibra- 
tion. Average  these  values  and  record  the  result.  Find 
the  time  of  one  vibration  of  the  pendulum  by  counting  it 
for  a  minute.  Several  trials  should  be  made  to  secure  its 
exact  rate.  Make  this  test  with  the  stylus  touching  the 
smoked-glass  plate.  Why  ?  Calculate  the  number  of 
vibrations  made  by  the  fork  per  second  from  your  data. 
Compare  your  result  with  the  value  stamped  on  the  fork 
by  its  maker. 

Conclusion.  —  What  might  cause  a  disagreement  between 
the  known  vibration-  rate  of  the  fork  and  the  value  you 
have  obtained  ?  Is  it  possible  to  change  the  vibration  rate 
of  a  fork  without  permanently  injuring  it  ?  What  kind  of 
motion  did  you  give  the  glass  ?  What  kind  of  motion  have 
the  pendulum  and  fork  ?  The  curves  you  traced  are  called 
sine  curves.  Compare  those  on  the  smoked  glass  with  the 
curves  plotted  in  Experiment  58.  Are  they  also  sine 
curves  ?  How  do  you  know  ? 

NOTE.  —  As  it  is  nearly  impossible  to  have  the  fork  stylus  and  the 
pendulum  stylus  coincide,  it  is  well  to  count  the  fork  vibrations  made 
during  two  vibrations  of  the  pendulum  and  divide  by  two.  This  elim- 
inates a  possible  source  of  error.  Why  ? 


SOUND 


109 


EXPERIMENT  64 

Object.  —  To  calculate  the  wave  lengths  of  the  sounds 
emitted  by  several  tuning  forks  at  the  temperature  of  the 
laboratory  and  to  compare  these  wave  lengths  with  the 
lengths  of  the  columns  of  air  which  reenforce  them. 

Apparatus.  —  A  set  of  heavy  tuning  forks  (C  =  256,  E  = 
320,  G  =  384,  and  C'  =  512),  a  glass  cylinder  about  2.5"  x 
1 8",  a  thermometer,  a  small  pitcher  of  water,  and  a  medi- 
cine dropper. 

Data.  - 


OBSERVATIONS 

C 

E 

G 

C' 

Vibration  frequency  of  fork       
Observed  length  of  resonating  air  column  . 
Correction  for  diameter  of  the  jar 
True  length  of  resonating  air  column 
Temperature  of  the  air  in  jar    
Velocity  of  sound  in  air  at  this  temperature 
Wave  length  of  sound  from  V  =  LN     .     . 
Wave  length  divided  by  resonating  column 

Directions.  —  Pour  or  drop  water  into  the  cylindrical  jar 
until  it  reenforces  the  sound  of  tuning  fork  C  =  256  most 
loudly.  Hold  the  fork  close  to  the  mouth  of  the  jar  with 
as  great  a  length  of  the  vibrating  prong  over  the  jar  as 
possible.  Care  should  also  be  taken  to  strike  the  fork 
against  a  book  or  other  soft  object,  always  with  the  same 
blow,  in  order  that  it  may  have  the  same  amplitude  of  vibra- 
tion each  time.  If  this  is  not  done,  the  true  length  of  the 
vibrating  column  may  not  be  determined.  Why  ?  In  the 


110  PHYSICAL   LABORATORY   GUIDE 

same  way  find  the  lengths  of  the  columns  that  best  ree'n- 
force  the  other  forks. 

Measure  the  internal  diameter  of  the  jar  carefully  and 
add  half  of  this  (its  radius)  to  the  observed  lengths,  to 
obtain  the  true  lengths  of  the  vibrating  air  columns.  Take 
the  temperature  of  the  air  in  the  room.  If  the  precaution 
has  been  taken  of  letting  the  water  used  stand  in  the  room 
long  enough  to  assume  the  room  temperature,  a  possible 
source  of  error  will  be  eliminated. 

Look  up  the  velocity  of  sound  in  air  at  o°  C.  and  the 
amount  this  velocity  is  increased  for  each  degree  Centi- 
grade above  zero,  and  calculate  its  value  in  centimeters 
per  second  for  the  temperature  of  the  laboratory. 

Next,  find  the  wave  length  for  each  fork,  using  the  fun- 
damental relation  that  velocity  =  wave  length  x  vibration 
frequency,  or  v  =  In. 

Finally,  find  the  ratio  of  the  wave  length  to  the  length 
of  resonating  column  for  each  fork. 

Conclusion.  —  What  is  your  average  value  for  the  wave 
length  divided  by  the  length  of  resonating  column  ?  What 
should  its  value  be  ?  Make  a  diagram  of  the  vibrating  fork 
and  its  resonating  air  column.  Referring  to  this  drawing, 
prove  that  your  answer  to  the  last  question  is  correct.  You 
have  noted  the  increase  in  the  velocity  of  sound  in  air  with 
a  rise  in  temperature.  Is  its  velocity  affected  by  changes 
in  the  amount  of  the  barometric  pressure  ?  Give  reasons 
for  your  answer. 

EXPERIMENT  65 

Object.  —  To  test  the  laws  for  the  vibration  of  strings. 

Apparatus.  —  A  sonometer,  weights  and  two  wooden 
prisms  for  bridges,  piano  wire,  sizes  22  and  28,  a  catgut 


SOUND 


III 


violin  string  the  same  diameter  as  the  22  piano  wire,  a 
set  of  tuning  forks  (C256,  E,  G,  and  C'),  a  meter  stick,  a 
micrometer  caliper. 

Data.  — 


VIBRATIONS 
PER  SECOND 
CALCULATED 

VIBRATIONS 
PER  SECOND 
BY  THE  FORK 

LENGTH  OF 
STRING 

DIAMETER 
OF  STRING 

TENSION 
ON  STRING 

SQ.  ROOT 
OF  TENSION 

Directions. — (a)  Using  the  28  piano  wire,  Adjust  the 
tension  until  the  open  string  vibrates  nearly  in  unison  with 
fork  C266.  The  tone  of  the  string  should  be  a  little  lower 
than  the  fork.  By  means  of  the  bridge  shorten  the  string, 
a  very  little  at  a  time,  until  it  and  the  fork  vibrate  in  uni- 
son. When  the  adjustment  is  nearly  right,  the  beats  may 
be  counted.  Continue  the  adjustment  until  the  beats  dis- 
appear. Measure  the  length,  diameter,  etc.,  of  the  string 
and  record  in  the  table. 

Without  changing  the  tension,  move  the  bridge  until  the 
length  of  the  string  is  just  half  what  it  was  before.  Com- 
pare the  tone  it  emits  under  these  conditions  with  the  tone 
of  the  C'512  fork. 

If  time  permits,  find  the  lengths  of  the  string  which  will 
vibrate  in  unison  with  forks  E  and  G. 

From  the  known  vibration  rate  of  the  C256  fork  and  the 
observed  lengths  of  the  strings  with  which  you  have  ex- 


112  PHYSICAL  LABORATORY   GUIDE 

perimented,  calculate  the  vibration  rates  of  the  last  three 
strings  used.  Do  this  by  an  inverse  proportion.  Com- 
pare these  vibration  rates  with  the  vibration  rates  of  the 
forks  which  vibrate  in  unison  with  them. 

(b)  Adjust  the  tension  and  length  as  in  (a)  of  the  22 
piano  wire  until  it  is  in  unison  with  fork   C256.      Adjust 
the  28  wire  to  exactly  the  same  length  and  tension.     With 
which  fork  is  this  string  now  in  unison  ?     What  kind  of  a 
proportion  exists  between  the  diameters  and  vibration  rates 
of  these  strings  ? 

(c)  Using  some  whole  number  of  pounds  tension,  adjust 
the  length  of  the  28  piano  wire  until  unison  is  established 
between  it  and  fork  C256.     Keeping  the  length  the  same, 
apply  four  times  the  tension.     With   which  fork  is  the 
string  now  in  unison  ?     Did   multiplying  the  tension  by 
four  also   increase   the   vibration   rate    to   four   times  its 
original  v^lue  ? 

(d)  Adjust  the  tension  and  length  of  the  22  piano  wire 
until  it  vibrates  in  unison  with  fork  C256.     Also  adjust  the 
gut  string  to  the  same  length  and  tension.    Which  gives  the 
higher  tone  ?    Approximately,  how  much  is  one  higher  than 
the  other  ?     Find  which  fork  is  more  nearly  in  unison  with 
the  second  string.     Which  string  has  the  greater  density  ? 
Which  has  the  greater  vibration  rate?     By  reference  to 
the  tables  in  Chapter  XI,  find  the  ratio  of  the  densities 
of  steel  and  gut.     Also  find  the  square  root  of  this  ratio. 

Conclusion.  —  State  the  known  laws  for  the  vibration  of 
strings.  Compare  your  data  with  these  laws.  State  how 
closely  you  have  proved  the  laws,  and  mention  some  of  the 
difficulties  to  be  overcome  if  the  actual  data  is  to  follow 
the  laws  exactly.  In  doing  this  consider  sections  a,  b,  c, 
and  d  separately. 


SOUND  113 

EXPERIMENT  66 
Object.  —  To  find  the  velocity  of  sound  in  air. 

Apparatus. — Two  revolvers  and  blank  cartridges  (a 
small  cannon  is  better  than  the  revolvers),  two  stop 
watches,  a  loo-ft.  tape,  and  two  thermometers. 

Directions.  —  This  experiment  should  be  performed  on 
some  level  ground  out  in  the  country  where  it  is  quiet. 
Select  two  stations  about  two  or  three  thousand  feet  apart. 
Measure  the  distance  between  them  accurately.  Divide 
the  class  into  two  squads,  and  let  one  squad  take  up  its 
position  at  each  station.  Each  station  is  provided  with 
one  stop  watch  and  one  revolver.  Let  one  of  the  members 
of  Squad  i  fire  his  revolver  and  one  member  of  Squad  2 
take  the  elapsed  time  between  the  appearance  of  the 
smoke  and  the  time  when  the  sound  reaches  his  ear. 
Next  let  a  member  of  Squad  2  fire  his  revolver  and  a 
member  of  Squad  I  time  the  sound.  Continue  signaling 
back  and  forth  in  this  way  until  each  member  of  the  class 
has  timed  the  sound  at  least  once.  It  will  be  well  to 
appoint  one  member  of  each  squad  to  act  as  recorder  and 
keep  a  record  of  the  results.  If  time  permits,  continue 
the  experimenting,  using  a  different  distance  between  the 
stations.  The  temperature  of  the  air  at  the  time  of  the 
experiment  should  be  carefully  observed  by  each  station. 
Also,  the  direction  of  the  wind  with  respect  to  the  direction 
of  the  line  joining  the  two  stations  should  be  recorded 
Record  all  results  in  tabular  form. 

Conclusion.  —  Calculate  the  velocity  of  sound  in  air  from 
each  observation  made.  Find  the  average  velocity  in  each 
direction.  One  of  these  will  probably  be  larger  and  the 


114  PHYSICAL   LABORATORY   GUIDE 

other  smaller  than  the  true  value.  Why  ?  Add  these 
average  velocities  in  each  direction  together  and  divide  by 
two.  Using  this  result  as  the  velocity  of  sound  in  air  at  the 
temperature  of  the  experiment,  calculate  the  velocity  for 
sound  in  air  at  o°  C.  Compare  this  value  with  the  known 
velocity  of  sound  in  air  at  o°  C.  as  given  in  your  textbook. 

NOTE. — A  Saturday  morning  or  afternoon  spent  by  teacher  and 
class  in  performing  this  experiment  will  be  found  to  well  repay  the 
effort  not  only  for  the  sake  of  the  experiment  itself,  but  because  of  the 
interest  it  will  awaken  in  scientific  research  in  general  on  account  of 
the  historic  interest  of  this  particular  experiment. 


CHAPTER    X 
NOTES   ON   THE   EXPERIMENTS 

FUNDAMENTAL  MEASUREMENTS 
(Chapter  I) 

I.  The  Law  of  Conservation  of  Matter  and  Energy. — 

Matter  and  energy  cannot  be  created  or  destroyed. 

Careful  measurements  extending  over  long  periods  of 
time,  and  dealing  with  many  different  substances  and  with 
all  the  known  forms  of  matter  or  energy,  show  that  the  dis- 
appearance of  a  given  quantity  of  either  is  always  followed 
by  the  formation  of  an  exactly  equivalent  quantity  of  some 
new  form. 

Thus  oxygen  and  hydrogen,  two  gases,  unite  chemically 
to  form  water.  Kinetic  energy  may  be  transformed  into 
heat  or  electrical  energy.  In  every  case,  however,  noth- 
ing is  lost.  The  sum  of  the  quantities  involved  before  any 
transformation,  either  of  matter  or  energy,  is  always  exactly 
equal  to  the  sum  of  the  products  formed.  An  appeal  to 
this  law  frequently  sheds  important  light  upon  the  investi- 
gation of  many  phenomena. 

II.  The  Laws  of  Capillary  Action.  — 

1.  Liquids  rise  in  tubes  when  they  wet  them,  and  their 
surface  is  concave  ;  they  are  depressed  in  tubes  when  they  do 
not  ivet  them,  and  their  surface  is  convex. 

2.  The  rise  or  depression  of  the  liquid  varies  inversely  as 
the  diameter  of  the  tube. 

"5 


Il6  PHYSICAL   LABORATORY   GUIDE 

3.  Increasing  the  temperattire  of  a  liquid  diminishes  its 
capillarity,  and  vice  versa. 

Capillary  phenomena  will  be  understood  when  the  forces 
involved  are  considered.  These  forces  are  three  in  number, 
as  follows : 

(a)  Adhesion,  a  molecular  force  of  attraction  acting  be- 
tween unlike  molecules  and  causing  an  upward  force  tend- 
ing to  lift  the  column  of  liquid  in  the  tube. 

(£)  Cohesion,  a  molecular  force  acting  between  like 
molecules  and  tending  to  draw  any  mass  of  liquid  into 
the  form  of  a  sphere.  It  is  evident  that  this  force  opposes 
the  force  of  adhesion  in  capillary  tubes. 

(c)  Gravity  is  the  mutual  attraction  between  any  body 
and  the  earth.  This  force,  according  to  the  laws  of 
gravity  pressure  in  fluids,  tends  to  keep  the  liquid  surfaces, 
within  and  outside  of  the  tube,  at  the  same  level.  (See 
laws  of  fluid  pressures  in  your  textbook.)  Evidently- 
this  force  also  opposes  the  rise  of  liquids  in  capillary 
tubes. 

Liquids  will  rise  then  under  the  force  of  adhesion  until 
this  force  is  balanced  by  the  combined  action  of  cohesion 
and  gravity,  when  the  liquid  column  will  remain  stationary. 
Since  the  weight  of  the  liquid  column  varies  with  the 
square  of  its  radius  while  its  surface  in  contact  with  the 
tube  varies  only  as  the  first  power,  liquids  will  not  rise  so 
high  in  tubes  of  large  diameter. 

Furthermore,  a  rise  in  temperature  increases  the  spaces 
between  the  molecules,  and  this  cuts  down  the  intensity 
of  the  molecular  forces  while  gravity  remains  practically 
unchanged.  Thus  an  increase  of  temperature  in  a  liquid 
necessarily  decreases  the  amount  of  capillarity. 

What  appears  to  be  a  double  surface  of  most  liquids 
where  they  come  in  contact  with  the  containing  vessel  is 


NOTES   ON   THE   EXPERIMENTS  117 

due   to    capillary   action.     Capillary   action   explains   the 
working  of  lamp  wicks,  blotters,   etc. 

III.  To  read  a  Fortin  Barometer.  —  The  barometer 
must  hang  vertically.  Read  the  temperature  at  once,  for 
otherwise  the  presence  of  the  body  of  the  observer  may 
vitiate  the  observation.  Tap  the  barometer  gently  near 
the  upper  level  of  the  mercury.  This  enables  the  menis- 
cus to  assume  its  proper  shape.  Adjust  the  level  of  the 
mercury  in  the  cistern.  To  do  this,  if  necessary,  lower  and 
then  raise  the  cistern  screw  until  the  level  of  the  mercurial 
surface  just  touches  the  tip  of  the  ivory  pointer.  This 
will  be  indicated  by  a  slight  depression  and  irregularity  of 
the  surface.  If  the  surface  is  bright  and  clean,  the  image 
of  the  pointer  will  be  seen  in  this  surface  by  reflection. 

Next  set  the  vernier.  The  bottom  of  the  vernier  must 
be  brought  so  as  to  be  an  apparent  tangent  to  the  convex 
surface  of  the  meniscus.  To  avoid  parallax,  advantage 
must  be  taken  of  the  movable  tube  on  which  the  vernier 
is  graduated.  The  back,  lower  edge  of  this  ought  to  coin- 
cide with  the  front,  lower  edge  when  viewed  from  the 
proper  position.  When  thus  set,  if  the  eye  be  moved 
slightly  up  and  down,  no  line  of  light  should  appear  in  the 
middle.  We  are  thus  sure  that  the  line  of  sight  is  hori- 
zontal. 

The  reading  may  now  be  observed  from  the  fixed  scale 
and  from  the  coincident  lines  on  the  vernier.  For  very 
accurate  work  a  number  of  corrections  should  be  applied 
to  the  observed  barometric  height  as  follows : 

(a)  Correction  for  temperature,  (<£)  correction  for  capil- 
larity, (c)  correction  for  errors  in  the  scale  graduations, 
(d)  correction  for  unequal  intensity  of  gravity,  (e)  reduc- 
tion to  sea  level. 


Il8  PHYSICAL  LABORATORY   GUIDE 

For  ordinary  labratory  wdrk  the  first  and  second  of  these 
only  need  be  considered.  Tables  giving  corrections  will 
be  found  in  Chapter  XL 

If  the  barometer  is  graduated  in  English  measure,  its 
temperature  correction  may  be  calculated  from  the  follow- 
ing formula : 

H=N--^-     (.09 /-  2.56 
1000 

where 

H  =  corrected  barometric  height, 

N  —  observed  barometric  height, 
/  =  the  temperature  of  the  barometer. 

Use  tables  in  Chapter  XI  to  correct  a  metric  barometer. 

IV.  The  Atmospheric  Pressure. — Galileo  (1564-1642) 
suspected  the  existence  of  an  atmospheric  pressure,  but 
died  before  proving  it.  His  pupil,  Torricelli,  not  only 
proved  the  existence  of  an  atmospheric  pressure,  but  also 
measured  its  amount  by  means  of  the  familiar  barometer 
tube  and  bowl  of  mercury. 

The  amount  of  this  pressure  is  constantly  varying,  but 
under  standard  conditions,  that  is,  a  mercury  column 
760  mm.  (29.92  in.)  high,  it  amounts  to  1033.3  gm-  per 
square  centimeter  (14.7  Ib.  per  square  inch).  The 
temperature  of  the  mercury  under  standard  conditions 
must  be  o°  C. 

A  liquid  boils  when  its  vapor  tension  (the  pressure  of 
the  vapor)  is  equal  to  or  slightly  exceeds  the  atmospheric 
pressure.  Its  vapor  tension  depends  upon  the  energy  of 
its  molecules,  and  hence  upon  its  temperature. 

It  is  evident,  then,  that  the  boiling  point  of  a  liquid  is  not 
a  constant  temperature,  but  depends  directly  upon  the 
amount  of  the  atmospheric  pressure. 

Scientists   have   agreed   to  call   the  temperature  of  the 


NOTES   ON   THE   EXPERIMENTS  119 

steam  from  water  boiling  under  standard  conditions  100°  C. 
Experiment  shows  that  a  rise  or  fall  of  I  cm.  in  the  baro- 
metric reading  changes  the  boiling  point  .37°  C.  (One  inch 
changes  it  .945°  C.)  The  variation  is  direct,  a  rising 
barometer  increasing  the  boiling  point,  and  vice  versa. 

By  noting  how  much  the  barometer  reads  above  or  below 
standard,  the  boiling  point  corresponding  to  this  pressure 
is  easily  calculated  from  the  data  just  given. 

For  an  accurate  determination  of  the  boiling  point  from 
the  observed  height  of  the  barometer  several  corrections 
must  be  applied  to  this  barometer  reading.  (See  Section 
III  on  the  Barometer;  also  the  tables  for  barometric  cor- 
rection in  Chapter  XL) 

DENSITY  AND  SPECIFIC  GRAVITY 
(Chapter  I) 

V.  Archimedes'  Principle. — A  body  immersed  in  a  fluid 
is  buoyed  up  by  a  force  equal  to  the  weight  of  the  fluid  it 
displaces  ;  or,  —  The  loss  of  weight  of  a  body  immersed  in  a 
fluid  is  equal  to  the  weight  of  the  displaced  fluid,  which  has 
the  same  volume  as  the  body. 

This  law  discovered  by  Archimecfes  (287-212  B.C.)  is 
particularly  interesting,  both  on  account  of  its  early  dis- 
covery and  because  of  its  wide  application.  Most  of  the 
methods  used  for  specific  gravity  determinations  depend 
upon  it.  In  fact,  Archimedes  was  trying  to  find  the 
amount  of  pure  gold  in  his  king's  crown  when  he  discov- 
ered it.  The  ascension  of  balloons  likewise  is  governed 
by  this  principle. 

VI.  The  Law  of  Flotation.  — A  floating  body  displaces  its 
own  iveight  of  the  liquid  in  which  it  floats. 

This  law  is  only  a  special  case  of  Archimedes'  principle, 

PHYS.  LAB.  GUIDE  —  9 


120  PHYSICAL   LABORATORY   GUIDE 

in  which  the  body  is  able  to  displace  a  volume  of  the  liquid 
which  weighs  as  much  as  the  body  itself.  The  construc- 
tion of  boats  and  of  hydrometers  depends  on  this  law. 

VII.  Pascal's  Law. — Pressure  exerted  upon    any  given 
area  of  a  liquid  inclosed  in  a  vessel  is  transmitted  undimin- 
ished  to  every  equal  area. 

The  laws  of  gravity  pressure  : 

(a)  The  pressure  is  directly  proportional  to  the  depth  of 
the  liquid. 

(b)  The  pressure  is  directly  proportional  to  the  density  of 
the  liquid. 

(c)  The  intensity  of  pressure  at  any  point  in  a  liquid  is 
the  same  in  all  directions. 

VIII.  Density  and  Specific  Gravity.  —  Density  is  the  mass 
per  unit  of  volume  of  a  substance.     The  usual  unit  of  mass 
is  the  gram,  and  the  unit  of  volume  is  the  cubic  centimeter. 
Density  then  is  the  mass  (or  weight)  of  one  cubic  centi- 
meter of  a  substance  measured  in  grams.     The  density  of 
water  is  one  gram. 

Specific  gravity  is  the  weight  of  a  given  quantity  of  a 
substance  compared  with  tJie  weight  of  tJie  same  volume  of 
water.  Hence,  the  specific  gravity  of  water  must  be  one. 

It  is  evident  that  the  density  and  the  specific  gravity  of 
any  substance  must  be  numerically  equal.  For  since  the 
weights  of  any  equal  volumes  of  the  substance  and  water 
when  compared  give  the  specific  gravity  of  the  substance, 
we  can  choose  the  weights  of  one  cubic  centimeter  of  each 
material.  But  the  weight  of  one  cubic  centimeter  of  water 
is  one  gram.  Dividing  the  density  of  a  substance  by  one 
does  not  alter  its  magnitude.  Thus,  the  density  and  the 
specific  gravity  of  any  substance  are  numerically  equal,  al- 


NOTES   ON   THE   EXPERIMEiNTS  121 

though  the  meaning  of  these  numbers  is  quite  different. 
The  same  argument  would  apply  to  equal  volumes  con- 
taining many  cubic  centimeters. 

In  determining  density  with  a  balance,  five  important 
cases  must  be  considered.  In  the  formulae  that  follow, 
the  symbols  used  have  the  following  meanings : 

W  =  the  weight  of  the  substance  in  air. 

W^  =  the  weight  of  the  substance  in  water. 

Wa  =  the   weight    of  the    substance    in    a    liquid    whose 

density  is  s. 

S  =  the  density  of  the  liquid  used  in  place  of  water. 
W<i  —  the  weight  of  the  body  and  sinker  together  in  water. 
Wi  =  the  weight  of  the  solid  in  the  liquid  whose  density 

is  required. 
b  —  the  weight  of  a  sinker  in  water. 

CASE  i.  When  the  solid  is  heavier  than  water  and  in- 
soluble in  that  liquid.  Then, 

D=        W        (i) 

W--  W^ 

The  denominator  of  this  fraction  is  the  loss  of  weight  of 
the  body  in  water,  and  this,  by  Archimedes'  principle,  is 
equal  to  the  weight  of  the  displaced  water.  Since  one 
cubic  centimeter  of  water  weighs  one  gram,  the  denomi- 
nator of  this  fraction  is  also  the  volume  of  the  displaced 
water  in  cubic  centimeters,  and  hence  the  volume  of  the 
body.  The  weight  of  the  body  divided  by  its  volume  will 
give  its  density.  (See  definition  of  density  given  above.) 

CASE  2.  When  the  solid  is  heavier  than  water,  but  dis- 
solves in  it.  Then, 

W 


W-  Ws^       WS 
5          "  W-  Ws 


122  PHYSICAL   LABORATORY   GUIDE 

Since  the  substance  is  soluble  in  water,  it  is  weighed  in 
another  liquid  of  known  density  in  which  it  will  not  dis- 
solve. 

Now  by  the  reasoning  of  Case  I,  W  —  Wsis  the  weight 
of  the  displaced  liquid.  If  this  is  divided  by  S,  the  weight 
of  one  cubic  centimeter  of  this  liquid,  the  quotient  will  be 
the  volume  of  the  displaced  liquid  and  also  the  volume  of 
the  body.  The  weight  of  this  body,  W,  divided  by  its 

W  —  Ify 

volume,  -  -  —  -,  gives  the  required  density. 
*j 

CASE  3.     When  the  solid  is  lighter  than  water.     Then, 

=  or 


w- 


The  parenthesis  (  W—  fr)  is  the  weight  of  the  solid  in 
water,  hence  subtracting  this  from  W  gives  the  volume 
of  the  body  as  in  Cases  I  and  2.  The  complete  formula 
is  evidently  the  density. 

The  pupil  should  give  the  steps,  with  reasons,  in  this 
case. 

CASE  4.     The  density  of  a  liquid,  using  a  density  bottle, 
Bottles  are  made  which  hold  exactly  100  c.c.  at  a  known 
temperature.     The  weight  of  liquid  held  by  such  a  bottle 
divided  by  100  is  obviously  the  density  required. 

If  an  ordinary  bottle  with  a  ground  glass  stopper  is 
used,  the  volume  of  liquid  it  will  hold  may  be  found  by 
obtaining  the  weight  of  the  water  in  it  when  it  is  filled. 
Each  gram  of  water  occupies  one  cubic  centimeter  of  space. 

CASE  5.  The  density  of  a  liquid  by  displacement. 
Here, 


NOTES   ON   THE   EXPERIMENTS  123 

If  a  solid  body  is  first  weighed  in  the  liquid  whose 
density  is  sought  and  the  same  solid  is  next  weighed  in 
water,  then  W—  Wt  is  the  weight  of  the  displaced  liquid. 
W—  W^  is  the  weight  of  water  displaced  by  the  same  body, 
and  hence  (see  Case  i)  is  the  volume  of  the  displaced 
liquid.  Dividing  the  weight  of  the  liquid  displaced  by  its 
volume  gives  its  mass  per  unit  of  volume  or  its  density. 

Similar  reasoning,  which  the  pupil  can  easily  supply 
after  he  has  mastered  the  above  cases,  will  prove  the 
formulae  given  to  be  true  for  specific  gravity  as  well  as 
density. 

VOLTAIC  CELLS   AND    THERMOCURRENTS.  —  ELECTRICAL 

TESTING 

(Chapters  IV  and  V) 

IX.  Voltaic  Cells.  —  A  simple  voltaic  cell.  Such  a  cell 
consists  of  a  zinc  and  a  copper  plate  immersed  in  dilute 
sulphuric  acid,  one  part  by  volume  of  acid  to  twenty  parts 
by  volume  of  water.  The  acid  should  be  poured  into  the 
ivater  with  constant  stirring.  When  the  circuit  is  closed, 
the  action  of  such  a  cell  is  as  follows : 

Zinc  +  sulphuric  acid  =  zinc  sulphate  4-  hydrogen, 
or  + 

Zn  +  H2SO4  =  ZnSO4  4-  H2 

The  hydrogen  particles  constantly  carry  plus  charges  to 
the  copper  plate,  while  the  zinc  sulphate  carries  minus 
charges  to  the  zinc  plate.  The  hydrogen  is  not  soluble 
in  the  acid  and  hence  collects  on  the  copper  plate.  This 
film  of  hydrogen  is  practically  a  non-conductor  and  in- 
troduces a  high  internal  resistance  in  the  cell  which  greatly 
weakens  the  current.  Besides,  the  film  of  hydrogen  acts 
like  a  hydrogen  plate.  The  e.  m.  f.  between  hydrogen  and 


124  PHYSICAL   LABORATORY    GUIDE 

zinc  is  in  the  reverse  direction  to  that  between  copper  and 
zinc.  Hence  the  hydrogen  sets  up  a  counter  e.  m.  f. 
which  greatly  weakens  the  e.  m.  f.  of  the  battery.  This 
trouble  from  the  hydrogen  sticking  to  the  copper  plate 
is  called  polarization  and  can  be  prevented  by  intro- 
ducing a  substance  which  will  unite  with  the  hydrogen 
chemically,  forming  with  it  some  soluble  compound.  This 
new  substance  is  called  a  depolarizing  agent. 

In  the  Daniell  cell,  copper  sulphate  is  the  depolarizing 
agent,  and  reacts  with  the  hydrogen  to  form  sulphuric  acid, 
according  to  the  equation  : 

H2  +  CuSO4  =  H2SQ4  +  Cu 

The  copper  (Cu)  set  free  carries  the  plus  charges  to  the 
copper  plate  and  there  is  itself  deposited  on  the  copper 
plate.  Thus  in  Daniell's  cell  the  copper  plate  grows  con- 
stantly heavier. 

In  the  Buns  en  cell  the  nitric  acid  (HNO3)  oxidizes  the 
hydrogen  to  water. 

In  the  Leclanche  cell  the  manganese  dioxide  (MnO2)  also 
oxidizes  the  hydrogen  to  water. 

Another  difficulty  with  the  simple  voltaic  cell,  known  as 
local  action,  is  due  to  the  presence  of  small  particles  of 
impurities  on  the  surface  of  the  zinc  plate.  These  im- 
purities are  usually  carbon,  iron,  or  copper.  Any  one  of 
these  substances  in  contact  with  the  zinc  plate,  immersed 
in  sulphuric  acid,  is  a  small  voltaic  cell.  The  plates  of  this 
small  cell  being  in  contact  cannot  contribute  anything  to 
the  external  or  useful  circuit.  However,  these  small  cells 
do  use  up  the  zinc  and  acid  and  therefore  are  wasteful. 
The  simple  and  universal  remedy  for  local  action  is  to 
amalgamate  the  zinc  plate.  This  alloy  of  mercury  and 
zinc,  called  zinc  amalgam,  is  a  soft  pasty  substance  which 


NOTES   ON   THE   EXPERIMENTS  125 

covers  over  the  impurities.  As  the  zinc  is  removed  from 
this  amalgam  by  the  action  of  the  acid,  the  mercury  dis- 
solves more  zinc.  Thus  the  process  is  continuous,  and 
very  little  mercury  is  required.  Zinc  plates  are  easily 
amalgamated  by  dipping  them  in  dilute  sulphuric  acid  and 
then  rubbing  on  the  mercury  with  a  cloth  also  wet  with 
the  acid. 

X.  The  Laws  of  Electrolysis.  — 

1 .  The  mass  of  an  electrolyte  decomposed  is  proportional 
to  the  quantity  of  electricity  which  passes  through  it. 

2.  The  mass  of  any  ion  liberated  by  a  given  quantity  of 
electricity  is  proportional  to  the  chemical  equivalent  of  the 
ion. 

Since  by  the  first  law  the  weight  of  any  substance 
deposited  by  an  electric  current  in  a  given  time  (current  x 
time  =  quantity  of  electricity  transferred)  is  directly  pro- 
portional to  the  strength  of  that  current,  this  law  has  been 
made  the  basis  of  a  method  for  measuring  current  strength. 
(See  Experiment  22  on  the  Study  of  a  Daniell  Cell;  also 
the  definition  of  an  ampere  given  under  XIII  in  this 
section.) 

The  chemical  equivalent  referred  to  in  the  second  law  is 
a  number  which  represents  the  mass  of  a  substance  which 
unites  chemically  with  one  gram  of  the  standard  substance 
hydrogen. 

The  electrochemical  equivalent  of  a  substance  is  the 
weight  in  grams  of  that  substance  deposited  in  one  second 
by  a  current  of  one  ampere.  (See  table  of  electrochemical 
equivalents  in  Chapter  XI.) 

XI.  The  Laws  of  Electrical  Resistance.  — 

I.  The  resistance  of  a  conductor  is  directly  proportional 
to  its  length. 


126  PHYSICAL   LABORATORY   GUIDE 

2.  The  resistance  of  a  conductor  is  inversely  proportional 
to  its  cross-sectional  area. 

3.  The  resistance  of  a  conductor  depends  upon  the  kind  of 
material  of  which  it  is  made  and  upon  the  molecular  con- 
dition of  this  material. 

4.  Metals  have  their  resistances  increased  by  increase  of 
temperature.     Carbon  and  most  electrolytes  decrease  in  re- 
sistance as  their  temperature  rises. 

The  specific  resistance  of  a  substance  is  the  resistance  in 
ohms  of  a  bar  of  the  substance  of  unit  length  and  unit 
cross  section.  In  the  metric  system  the  unit  of  length 
usually  chosen  is  the  meter  and  the  cross-sectional  area 
that  of  a  round  wire  one  millimeter  in  diameter. 

In  the  English  system  the  length  chosen  is  the  foot  and 
the  cross-sectional  area  that  of  a  round  wire  one  mil  in 
diameter.  The  mil  is  the  one  thousandth  part  of  an  inch. 
The  values  for  the  commoner  substances  are  given  in 
Chapter  XI  'expressed  in  both  systems. 

The  resistance  of  any  conductor  is  found  by  applying 
the  formula: 


in  which  R  —  the  total  resistance  in  ohms, 

k  —  specific  resistance  of  the  substance, 
/  =  the  length  of  the  wire, 
d  —  the  diameter  of  the  wire. 

The  temperature  coefficient  of  a  substance  is  the  amount 
one  ohm  of  it  changes  in  resistance  when  heated  or  cooled 
one  degree  Centigrade.  (See  table  in  Chapter  XL) 

XII.  Ohm's  Law.  The  current  flowing  in  any  electrical 
conductor  is  directly  proportional  to  the  difference  of  potential 
of  the  ends  of  this  conductor  divided  by  its  resistance.  In 
algebraic  form  : 


NOTES   ON    THE   EXPERIMENTS  127 

C  =  f,  or  Amperes  =^ 
R  Ohms 

A  special  case  of  Ohm's  law  very  convenient  when  ar- 
ranging voltaic  cells  in  batteries  is  as  follows : 

SE 


where      5  =  the  number  of  cells  in  series, 
E  =  the  e.  m.  f.  of  each  cell, 
r=  the  internal  resistance  of  each  cell, 
P  =  the  number  of  sets  of  cells  in  parallel, 
R  —  external  resistance. 

The  greatest  current  output  is  obtained  from  any  battery 
when  the  cells  are  so  arranged  that  the  internal  resistance 
of  the  battery  is  equal  to  the  external  resistance  of  the 

Sr 
circuit.     This   condition  is  fulfilled  when  —  =  R   in  the 

formula. 

XIII.  Electrical  Units.  —  The  ampere,  the  ohm,  and  the 
volt.  The  unit  of  current  strength  is  the  ampere.  It  is 
that  current  which  will  deposit  by  electrolysis,  under  suit- 
able conditions,  .001118  gm.  of  silver  in  one  second.  The 
ampere  will  deposit  4.025  gm.  of  silver  per  hour. 

The  ohm  is  the  unit  of  resistance.  The  resistance  of  a 
column  of  pure  mercury  106.3  cm-  l°ng  and  i  sq.  mm. 
in  cross  section  when  at  a  temperature  of  o°  C.  is  equal 
to  one  ohm.  This  is  the  standard  International  Ohm. 

The  volt  is  the  unit  of  electromotive  force  or  potential 
difference.  That  e.  m.  f.  which  will  cause  a  current  of  one 
ampere  to  flow  through  a  circuit  whose  resistance  is  one 
ohm  is  called  one  volt. 


128  PHYSICAL   LABORATORY   GUIDE 

XIV.  Galvanometers.  —  These  instruments  are  used  to 
detect  and  to  compare  small  electric  currents.  Practically, 
all  forms  work  on  the  principle  discovered  by  Oersted  in 
1816:  that  a  conductor  carrying  an  electric  current  has 
magnetic  properties  and  can  be  made  to  deflect  a  magnetic 
compass  needle. 

(a)  The  tangent  galvanometer.     This  form  consists  of  a 
large  vertical  coil  of  wire  with  a  relatively  small  magnetic 
needle  pivoted  on  a  vertical  axis  at  the  center  of  this  coil. 
To  use  this  instrument  the  plane  of  the  vertical  coil  must 
coincide  with  the  magnetic  meridian  and  the  zero  of  the 
compass  scale  must  be  directly  under  the  north-seeking  end 
of  the  needle.     This  instrument  is  called  a  tangent  galva- 
nometer because  the  current  passing  through  it  is  propor- 
tional to  the  tangent  of  the  angle  of    deflection  of  the 
needle.     (See  the  table  of  natural  trigonometric  tangents 
given  in  Chapter  XL) 

(b)  The  D' Arsonval  galvanometer.     This  instrument  con- 
sists of  a  powerful,  compound,  horseshoe,  permanent  mag- 
net supported  vertically.     Between  the  poles  of  this  magnet 
is  suspended  a  light  coil  consisting  of  many  turns  of  very 
fine,  insulated  wire.     Inside  of  this  movable  coil  is  a  sta- 
tionary cylinder  of  soft  iron  to  increase  the  permeability 
of  the  magnetic  circuit.     The  current  is  led  into  and  out 
of  the  movable  coil  by  means  of  the  top  and  bottom  sus- 
pending wires,  which  are  usually  of  bronze.     Various  de- 
vices are  used  for  observing  the  motion  of  the  movable  coil. 
One  of  the  best  consists  of  a  small  mirror  attached  to  the 
coil.     When  a  beam  of  light  is  reflected  from  this  mirror  to 
a  distant  scale,  the  motion  of  the  spot  of  light  serves  as  a 
pointer.     The  great  advantage  of  this  method  is  that  a  very 
long  pointer  can  be  used,  making  the  galvanometer  very 
sensitive  without  increasing  the  weight  of  the  moving  parts. 


NOTES    ON   THE    EXPERIMENTS  I2Q 

Compare  D'Arsonval's  galvanometer  with  the  tangent 
form,  and  note  that  the  principle  in  both  is  the  same.  In 
the  D'Arsonval  galvanometer  the  coil  moves  and  the  mag- 
net is  stationary.  The  reverse  is  true  in  the  tangent  and 
astatic  forms. 

(c)  The  astatic  galvanometer.  In  this  instrument  the 
coil  of  wire  is  horizontal  and  stationary.  The  movable 
part  consists  of  two  magnetic  needles  of  equal  strength 
firmly  fastened  to  a  vertical  wire  so  that  they  are  parallel. 
Their  like  poles  point  in  opposite  directions.  This  mag- 
netic system  is  suspended  by  a  silk  fiber  in  such  a  way 
that  the  lower  needle  turns  within  the  coil  and  the  upper 
needle  just  above  it.  A  light  pointer  shows  the  motion  of 
the  needles  upon  a  horizontal  scale.  If  the  needles  are 
carefully  made  of  equal  strength,  this  instrument  is  not 
affected  by  magnetic  fields  outside  of  its  own  field. 

In  all  three  forms  of  galvanometer  just  described,  the 
principle  is  the  same.  When  a  current  is  passed  through 
any  one  of  the  three  forms,  two  magnetic  fields  exist,  one 
of  which  is  free  to  turn  against  the  torsional  force  of  the 
suspension.  The  reaction  of  these  fields  causes  the  deflec- 
tion which  is  read  in  degrees.  The  principle  is :  Like 
poles  repel  and  unlike  poles  attract. 

XV.  The  Wheatstone  Bridge.  — This  apparatus  for  meas- 
uring the  resistance  of  a  conductor  consists  of  four  resist- 
ances arranged  as  the  four  sides  of  a  diamond  (or  any 
quadrilateral).  The  galvanometer  and  battery  are  con- 
nected as  shown  in  Figure  13.  Let  the  known  resistances 
be  rlt  r2,  and  R  and  call  the  unknown  resistance  x.  The 
diagram  shews  how  these  are  arranged.  It  is  usual  to 
make  the  possible  values  of  r^  and  r2,  called  the  ratios, 
multiples  of  ten,  as  i,  10,  100,  etc.,  whereas  R  can  have 


130 


PHYSICAL  LABORATORY   GUIDE 


any  value  varying  by  single  ohms  from  one  ohm  up,  de- 
pending on  the  desired  capacity  of  the  bridge. 

When  the  bridge  is  so  adjusted  that  no  current   flows 
through  the  galvanometer,  it  is  said  to  be  balanced.     The 


FIG.  13. 

points  a  and  d  are  then  at  the  same  potential.  Hence  the 
difference  of  potential  between  a  and  b,  and  b  and  <//is  the 
same.  Call  it  E^.  In  like  manner  the  difference  of  poten- 
tial between  a  and  c,  and  c  and  d,  is  the  same.  Call  it  £2. 

Since  no  current  passes  through  the  galvanometer,  the 
currents  in  ba  and  ac  are  equal.  Call  them  Cv  Also  call 
the  currents  in  bd  and  dc,  C%. 

If  Ohm's  law  is  now  applied  to  these  circuits,  the  follow- 
ing relations  are  obtained : 


NOTES   ON    THE   EXPERIMENTS  131 


also  C*  =  g      ,f  =  f  .........    (2) 

~ 


Dividing  (i)  by  (2)  we  have, 

x      R 

. —  =  — - 

r\      ri 


(3) 


That  is,  when  a  Wheatstone  bridge  is  balanced,  the  four 
resistances  are  in  direct  proportion.  From  equation  (3) 
the  value  of  #  is  easily  found. 

THE  MECHANICS  OF  SOLIDS 

(Chapter  VI) 

XVI.  Hooke's  Law.  —  Within  the  elastic  limit  the  strain 
produced  in  a  body  is  directly  proportional  to  the  stress 
applied. 

(a)  A  stress  is  two  or  more  balanced  forces.     It  causes 
a  bending,  twisting  elongation  or  compression  of  the  body. 

(b)  A  strain  is  the  change  of  shape  caused  by  a  stress. 

(c)  Elasticity  is  that  property  of  matter  which  enables  it 
to  regain  its  original  shape  or  volume  upon  the  removal  of 
the  stress. 

(d)  The  elastic  limit  of   a  body  is  the   point   beyond 


132  PHYSICAL   LABORATORY    GUIDE 

/ 

which  it  is  unable  to  regain  its  former  shape  or  volume 
when  the  stress  is  removed.  Elastic  limit  is  usually 
measured  in  pounds  per  square  inch  or  grams  per  square 
centimeter. 

(e)  The  modulus  of  elasticity  is  the  ratio  of  the  stress  to 
the  strain,  or,  what  amounts  to  the  same  thing,  it  is  the 
calculated  stress  necessary  to  double  the  length  of   the 
body.     Although  most  substances  will  not  allow  of  such 
an   elongation,    nevertheless   these   moduli  are   useful  in 
comparing  the  elasticities  of  various  substances.     They  are 
usually  given  in  pounds  per  square  inch  or  in  dynes  per 
square  centimeter. 

(f)  The  ultimate,  tensile  strength  of  a  substance  is  the 
number  of   pounds   necessary  to  break    a  bar  of  it  one 
square  inch  in  cross  section.     Sometimes  it  is  measured  in 
grams  or  kilograms  per  square  centimeter. 

XVII.  The  Parallelogram  Law.  —  If  upon  two  concm  rent 
forces,  as  sides,  a  parallelogram  be  constructed  to  some 
scale,  the  concurrent  diagonal  of  this  parallelogram  will 
represent  the  resultant  of  these  two  forces  both  in  direction 
and  magnitude. 

Some  definitions : 

Concurrent  forces  are  those  having  a  common  point  of 
application. 

Two  or  more  forces  acting  upon  the  same  body  are 
called  component  forces. 

A  single  force  exactly  equivalent  to  two  or  more  com- 
ponent forces  and  capable  of  replacing  these  forces  and 
producing  the  same  effect  is  called  a  resultant. 

A  force  exactly  equal  to  the  resultant  in  magnitude, 
but  opposite  to  it  in  direction  and  having  the  same  point 
of  application,  is  called  an  equilibrant. 


NOTES   ON   THE   EXPERIMENTS  133 

XVIII.  The  Laws  of  Parallel  Forces. 

(a)  The  magnitude  of  the  resultant  of  two  parallel  forces 
is  equal  to  their  algebraic  sum. 

(b)  The  direction  of  the  resultant  of  two  parallel  forces  is 
that  of  the  larger  component. 

(c)  The  point  of  application  of  the  resultant  of  two  parallel 
forces  divides  the  line  joining  the  two  forces  into  two  parts 
wJiicJi  are  inversely  proportional  to  the  forces  themselves. 

Note  that  problems  involving  parallel  forces  may  also  be 
solved  by  applying  the  general  law  of  moments.  See  section 
following. 

XIX.  The  General  Law  of  Moments.  —  If  a  body  is  in 
equilibrium,  the  sum  of  the  moments  tending  to  produce  rota- 
tion of  that  body  about  any  point  in  one  direction  is  equal 
to  the  sum  of  the  moments  tending  to  rotate  the  body  in  the 
opposite  direction  about  the  same  point. 

Definitions : 

(a)  The  moment  of  a  force  is  the  product  of  the  magni- 
tude of  that  force  and  its  perpendicular  distance  from  the 
axis  about  which  the  body  is  free  to  turn.     This  distance 
is  called  the  arm  of  the  force. 

(b)  Rest  means  zero  velocity.    Equilibrium  means  simply 
zero  acceleration.     A  body  revolving  uniformly  in  a  circle 
is  in  equilibrium. 

XX.  Newton's  Law  of  Universal  Gravitation.  —  Every 
particle  of  matter  in  the  universe  attracts  every  other  particle 
with  a  force  whose  direction  is  that  of  a  line  joining  the  two 
particles,  and  whose  magnitude  varies  directly  as  the  product 
of  the  two  masses,  and  inversely  as  the  square  of  the  distance 
betiveen  them. 

The  weight  of  a  body  is  then  but  a  special  case  of  the 


134  PHYSICAL   LABORATORY   GUIDE 

universal  law  just  stated,  and  may  be  denned  as  the  mutual 
attraction  between  that  body  and  the  earth. 

A  body's  weight  is  not  a  constant  quantity,  but  depends 
upon  the  relative  position  of  that  body  with  respect  to  the 
center  of  the  earth.  Since  the  polar  diameter  of  the  earth 
is  26^  mi.  less  than  its  equatorial  diameter,  it  follows  from 
Newton's  law  that  a  body  has  its  greatest  weight  at  the 
poles,  since  at  these  points  it  is  nearest  the  earth's  center. 
The  loss  of  weight  suffered  by  a  body  when  carried  from 
the  poles  to  the  equator  is  about  one  half  of  one  per  cent. 
(See  values  of  acceleration  due  to  gravity  in  the  table, 
Chapter  XL) 

(a)  Carrying  a  body  above  or  below  the  earth's  surface 
also   decreases    its    weight    according    to    the    following 
laws : 

1 .  The  weight  of  a  body  above  the  surface  of  the  -earth 
varies  inversely  as  the  square  of  the  distance  between  the  body 
and  the  earths  center.     (A  special  case  of  Newton's  law  of 
gravitation.) 

2.  The  weight  of  a  body  below  the  earths  surface  varies 
directly  with  the  distance  from  the  earths  center. 

(b)  According  to  Newton's  law,  every  molecule  in  a  body 
is  acted  upon  by  gravity,  and  these  forces  are  all  sensibly 
parallel,  since  they  point  toward  the  center  of  the  earth, 
4000  mi.  away.     From  the  laws  of  parallel  forces  the  mag- 
nitude of  their  resultant  would  be  their  sum,  or  equal  to 
the  weight  of  the  body.     If  this  single  force  is  to  be  a  true 
resultant,  it  must  be  applied  at  the  center  of  gravity  of  the 
body.      Hence,  center  of  gravity  may  be   denned  as  the 
point  of  application  of  the  resultant  of  all  the  parallel  forces 
of  gravity  acting  upon  the  body.     The  direction  of  these 
forces  of  gravity  acting  toward  the  center  of  gravity  of  the 
earth  is  called  a  vertical  line  or  a  plumb  line. 


NOTES   ON   THE   EXPERIMENTS  135 

(V)  The  space  passed  over  by  most  falling  bodies  is 
small.  Over  this  limited  space  the  force  of  gravity  is  con- 
stant, and  therefore  the  motion  of  a  falling  body  is  uni- 
formly accelerated;  that  is,  the  increase  in  velocity  per  unit 
of  time  is  a  constant  quantity.  Where  motion  is  of  this 
kind, 

•v  =  gt  and  s  =  |  gfi 

where       v  =  the  velocity  at  the  end  of  time  /, 
g  =  the  acceleration, 
/  =  the  time  in  seconds, 
s  =  the  space  passed  over  in  the  time  t. 

(d)  When  a  projectile  is  fired  vertically  upward  or 
downward,  its  actual  motion  is  the  resultant  of  the  uniform 
motion  (with  constant  velocity)  due  to  the  force  of  the 
powder  and  the  uniformly  accelerated  motion  due  to  grav- 
ity. As  the  velocities  act  along  the  same  straight  line, 
their  resultant  will  be  their  algebraic  sum.  When  the 
projectile  is  fired  horizontally,  the  components  due  to  the 
powder  and  gravity  act  at  right  angles.  Since  the  com- 
ponent due  to  gravity  is  continually  increasing  in  velocity 
while  the  other  is  constant,  the  actual  path  of  the  projec- 
tile will  be  a  curved  line  and  cannot  be  found  by  the 
parallelogram  law.  If,  however,  the  horizontal,  uniform 
component  of  the  projectile's  motion  is  plotted  along  an 
axis  of  x,  and  its  vertical  component,  due  to  gravity,  is 
plotted  along  the  axis  of  y,  then  the  curve  obtained  by 
combining  these  motions  as  directed  in  Experiment  41  will 
be  the  actual  path  followed  by  the  projectile.  This  curve 
will  always  be  a  parabola. 

XXI.   Newton's  Laws  of  Motion. 

I.  A  body  at  rest  ivill  remain  at  rest  forever,  and  a 
body  in  motion  will  continue  to  move  on  with  uniform 

PHYS.  LAB.  GUIDE — IO 


136  PHYSICAL   LABORATORY   GUIDE 

motion   in   a  straight  line  forever,    unless   acted  upon   by 
some  force  outside  of  itself  . 

2.  Change  of  momentum  is  directly  proportional  to  the 
impressed  force  and  takes  place  along  the  line  of  action  of 
this  force. 

3.  To  every  action  {force)  there  is  always  an  equal  and 
contrary  reaction  {force). 

Force  is  that  which  tends  to  change  either,  (a)  the  size  or 
shape  of  a  body,  or  (b)  the  state  of  rest  or  motion  of  a  body. 

There  are  many  quantities  dealt  with  in  physics  the 
exact  nature  of  which  we  do  not  know.  Force  is  one  of 
these,  hence  we  can  only  know  it  by  its  effects. 

From  the  second  law  of  motion  we  may  write  Fo——, 
since  —  -  is  rate  of  change  of  momentum.  Also  F^=  Ma 
for  a  =  -.  If  the  unit  of  force  is  properly  chosen,  we 


may  write  F=-  (i)   and  F  =  Ma  (2).       In  the  centi- 

meter, gram,  second  (or  C.  G.  S.)  system,  three  fundamen- 
tal units  are  chosen,  and  from  these  other  units  are  derived. 

The  centimeter,  the  unit  of  length  is  the  one  hundredth 
part  of  a  meter.  The  gram,  the  unit  of  mass,  is  the  quan- 
tity of  material  contained  in  one  cubic  centimeter  of  pure 
water  at  4°  C.  Water  has  its  greatest  density  at  this  tem- 
perature. The  second,  the  unit  of  time,  is  the  eighty-six 
thousand  four  hundredth  part  of  a  mean  solar  day. 

From  these  three  simple  quantities  many  other  units  are 
derived.  Some  of  these  follow.  The  C.  G.  S.  unit  of 
velocity  is  the  centimeter  per  second. 

Mv 
If    in   the  formula  F  —  -  the  values  one  gram,  one 


NOTES   ON   THE   EXPERIMENTS  137 

centimeter  per  second,  and  one  second  are  substituted  for 
m,  v,  and  /,  the  resulting  value  of  Fis  called  one  dyne,  the 
C.  G.  S.  unit  of  force. 

The  dyne,  then,  is  that  force  which  if  it  acts  for  one 
second  upon  a  mass  of  one  gram  will  give  it  a  change  in 
velocity  of  one  centimeter  per  second. 

By  substituting  in  the  well-known  formula  for  work, 
W=  F  x  vS,  one  dyne  for  /^and  one  centimeter  for  S,  we 
have  for  W,  the  work  done,  called  one  erg,  the  C.  G.  S. 
unit  for  measuring  either  work  or  energy. 

Since  the  erg  is  a  very  small  amount  of  work,  the 
joule,  equal  to  ten  million  (io7)  ergs,  is  frequently  more 
convenient. 

Power  or  rate  of  doing  work  in  the  C.  G.  S.  system  is 
work  done  at  the  rate  of  one  joule  per  second  and  is  called 
one  watt. 

Summary : 

The  centimeter  is  the  unit  of  length. 

The  gram  is  the  unit  of  mass.^ 

The  second  is  the  unit  of  time. 

The  centimeter  per  second  is  the  unit  of  velocity. 

The  dyne  is  the  unit  of  force. 

The  erg  is  the  unit  of  work  and  energy. 

The  joule  (io7  ergs)  is  the  unit  of  work  and  energy. 

The  watt  is  the  unit  of  power. 

XXII.  Boyle's  Law.  —  Under  a  constant  temperature  the 
volume  of  a  given  mass  of  gas  varies  inversely  as  the 
pressure  to  which  it  is  subjected ;  thus  Vl:  V^  =  P2  :  Plt  or, 

The  product  of  the  pressure  and  the  volume  of  a  given 
mass  of  gas  is  a  constant  quantity,  provided  the  temperature 
does  not  change ;  thus  P^  V^  —  P2  V^  is  a  constant  for  the 
same  mass  of  gas  tinder  constant  temperature. 


138  PHYSICAL   LABORATORY   GUIDE 

While  this  law,  discovered  by  Robert  Boyle  (1662),  is 
accurate  enough  for  all  ordinary,  practical  purposes,  care- 
ful tests  have  shown  that  it  is  not  perfectly  exact.  For 
example,  if  the  pressure  on  a  given  mass  of  air  is  steadily 
increased  from  i  to  78  atmospheres,  the  value  of  P  Fstead- 
ily  changes  from  I  to  .98.  Thereafter  the  value  of  PV 
increases  until  under  a  pressure  of  3000  atmospheres,  its 
value  is  4.2.  It  is  interesting  to  note  that  under  this  high 
pressure  the  density  of  air  is  .93,  nearly  equal  to  that  of 
water,  which  is  I.  With  more  easily  liquefiable  gases  such 
as  carbon  dioxide  the  departure  from  Boyle's  law  is  even 
greater  than  in  the  case  of  air. 

XXIII.   The  Laws  of  the  Pendulum.  — 

1 .  The  time  of  one  vibration  is  independent  of  the  ampli- 
tude, if  the  latter  is  small. 

2.  The  time  of  one  vibration  is  directly  proportional  to 
the  square  root  of  the  length. 

3.  The  time  of  one  vibration  is  inversely  proportional  to 
the  square  root  of  the  acceleration  due  to  gravity. 

Galileo  (1564-1642)  discovered  the  laws  of  the  pendu- 
lum. His  attention  was  first  brought  to  this  subject  by 
observing  the  oscillations  of  a  lamp  suspended  by  a  long 
rope  from  the  roof  of  the  cathedral  of  Pisa. 

The  motion  of  a  pendulum  is  periodic ;  that  is,  it  repeats 
itself  in  equal  time  intervals.  Note  also  that  each  time, 
it  swings  from  one  extreme  of  its  path  to  the  other,  it  has 
at  some  time  during  its  travel  three  different  kinds  of 
motion.  Its  motion  at  first  is  accelerated,  not  uniformly 
accelerated,  for  the  component  of  gravity  in  the  direction 
of  its  path  is  not  constant,  but  a  constantly  decreasing  force. 
The  value  of  this  component  reaches  zero  when  the  pen- 
dulum reaches  the  center  of  its  path.  Hence  for  an 


NOTES    ON   THE   EXPERIMENTS  139 

instant  its  motion  is  uniform.  The  motion  is  then  retarded 
until  the  pendulum  reaches  the  limit  of  its  swing. 

The  pupil  should  draw  the  pendulum  in  several  posi- 
tions in  its  path  and  plot  the  component  of  gravity  caus- 
ing its  motion  in  each  case,  and  note  how  this  component 
varies  in  intensity. 

The  laws  given  above  apply  only  to  a  simple  pendulum 
in  which  the  cord  is  practically  weightless  and  the  mass 
of  the  bob  is  concentrated  in  a  very  small  space. 

A  compound  pendulum  is  best  considered  to  be  a  vast 
number  of  simple  molecular  pendulums  rigidly  bound 
together  by  cohesion.  It  is  evident  that  the  molecules 
near  the  support  tend  to  vibrate  rapidly,  whereas  those 
most  remote  from  the  point  of  suspension  would  naturally 
have  a  much  longer  vibration  period.  Since  all  are  vibrat- 
ing together,  the  period  of  vibration  of  the  pendulum  will 
be  somewhere  between  these  two  extremes.  Somewhere, 
then,  in  the  pendulum  there  must  be  a  molecule  whose 
natural  period  of  vibration  as  a  simple  pendulum  would 
be  the  same  as  the  time  of  vibration  of  our  compound 
pendulum.  The  point  where  this  molecule  is  situated  is 
called  the  center  of  oscillation  of  the  pendulum. 

Huygens  first  showed  that  the  centers  of  suspension 
and  oscillation  were  interchangeable  without  making  any 
change  in  the  vibration  rate  of  the  pendulum. 

The  relations  given  in  Laws  (i)  and  (2)  may  be  ex- 
pressed algebraically  by  the  formula  : 

•-*>£ 

where  /  =  the  time  of  one  vibration, 


/  =  the  length  of  the  pendulum, 
g  —  the  acceleration  due  to  gravity. 


140  PHYSICAL  LABORATORY   GUIDE 

XXIV.  The  Laws  of  Sliding  Friction.  - 

1 .  Sliding  friction  is  very  nearly  independent  of  the  speed. 

2.  Sliding  friction  is  independent  of  the  area  of  the  sur- 
faces in  contact,  unless  this  area  is  so  small  that  one  surface 
cuts  into  the  other. 

3.  Sliding  friction  is  directly  proportional  to  the  amount 
of  pressure  between  the  surfaces  in  contact. 

4.  Sliding  friction  depends  upon  the  kinds  of  surfaces  in 
contact. 

Friction  is  an  opposing  force.  When  this  force  is 
moved  through  space,  work  is  done.  This  is  seldom,  if 
ever,  useful  work,  but  is  transformed  into  heat  and  wasted. 

The  use  of  roller  and  ball  bearings  in  machinery,  and 
the  application  of  lubricating  oils  which  really  constitute 
molecular  rollers,  will  greatly  reduce  the  energy  losses  due 
to  friction. 

The  amount  of  this  force  of  friction  for  any  two  sliding 
surfaces  is  measured  by  their  coefficient  of  friction.  This 
coefficient  is  equal  to  the  friction  divided  by  the  pressure. 
By  the  third  law  the  coefficient  is  a  constant  quantity  for 
the  same  two  surfaces,  since  the  friction  and  the  pressure 
are  directly  proportional. 

HEAT 
(Chapter  VII) 

XXV.  Heat.  —  Some  important  definitions  : 

(a)  Heat  is  a  form  of  energy.     According  to  the  kinetic 
theory  the  molecules  of  every  body  are  constantly  in  mo- 
tion.    This  motion  may  be  of  a  simple  vibratory  nature,  or 
it  may  be  exceedingly  complex  and  irregular.     Any  in- 
crease in  the  energy  of  these  molecular  motions  increases 
the  temperature  of  the  body. 

(b)  Temperature  is  the  thermal  condition  which  deter- 


NOTES   ON  THE   EXPERIMENTS  141 

mines  the  direction  and  rate  of  transfer  of  heat  energy 
from  one  body  to  another.  It  is  analogous  to  the  pressures 
in  liquids  and  gases  or  the  potential  difference  of  various 
parts  of  an  electric  circuit. 

(<:)  The  linear  coefficient  of  expansion  of  a  solid  is  the 
amount  one  unit  of  its  length  increases  in  length  when 
heated  i°  Centigrade. 

(d)  Just  as  the  degree  Fahrenheit  or  the  degree  Centi- 
grade is  the  unit  of  temperature  or  heat  intensity,  just  so 
the  calorie  measures  the  quantity  of  heat  energy.      The 
calorie  is  the  amount  of  heat  necessary  to  raise  I  gram  of 
water  i°  centigrade  in  temperature. 

(e)  Specific  heat  of  any  substance  is  the  number  of  calo- 
ries of  heat  necessary  to  raise  the  temperature  of  I  gram 
of  the  substance  i°  centigrade. 

(/)  The  thermal  capacity  of  any  body  is  the  total  amount 
of  heat  in  calories  necessary  to  raise  the  temperature  of 
the  entire  body  i°  centigrade.  It  is  calculated  by  multi- 
plying the  mass  of  the  body  in  grams  by  its  specific  heat 
in  calories.  This  product  is  sometimes  called  the  water 
equivalent  of  the  body,  because  it  not  only  is  the  amount 
of  heat  necessary  to  raise  the  body  i°  centigrade,  but  it  is 
also  the  weight  of  water  which  would  require  the  same 
amount  of  heat  to  raise  its  temperature  i°  centigrade  that 
the  body  requires. 

(g)  The  latent  heat  of  fusion  of  a  substance  is  the  num- 
ber of  calories  of  heat  required  to  change  I  gram  of  the 
substance  from  the  solid  to  the  liquid  state  without  change 
of  temperature. 

(/z)  The  latent  heat  of  vaporization  of  a  substance  is  the 
number  of  calories  of  heat  required  to  change  I  gram  of 
the  substance  from  the  liquid  to  the  gaseous  state  without 
change  of  temperature. 


142  PHYSICAL   LABORATORY   GUIDE 

(i)  The  dew  point  is  that  temperature  at  which  the 
aqueous  (water)  vapor  present  in  the  atmosphere  is  just 
sufficient  to  saturate  it.  It  is  that  temperature  to  which 
if  the  air  were  cooled  its  relative  humidity  would  become 
100  per  cent. 

(/  )  Relative  humidity  is  the  ratio  of  the  weight  of  water 
vapor  in  a  given  quantity  of  air  to  the  greatest  weight  of 
water  vapor  which  the  same  quantity  of  air  could  hold. 
Since  the  capacity  of  the  air  to  hold  water  vapor  increases 
with  the  temperature,  it  is  evident  that  relative  humidity 
depends  both  upon  the  actual  quantity  of  aqueous  vapor 
present  and  upon  the  temperature. 

LIGHT 
(Chapter  VIII) 

XXVI.    Light.  —  Important  laws  and  definitions  : 
(a)  Laws  of  intensity.  —  The  intensity  of  light  upon  any 
area  of  the  surface : 

1.  Varies  directly  as  the  illuminating  power  of  the  source. 

2.  Varies  inversely  as  the  square  of  the  distance  from  the 
area  to  the  source. 

3.  Diminishes  as  the  inclination  of  the  surface  to  the  rays 
of  light  increases. 

(£)  The  law  of  candle  power.  The  illuminating  powers 
of  two  sources  are  directly  proportional  to  the  squares  of  their 
distances  from  a  surface  which  they  illuminate  with  equal 
intensity. 

(c)  The  law   of   reflection.      The  angle   of  reflection   is 
equal  to  the  angle  of  incidence,  and  the  two  angles  are  in 
the  same  plane. 

(d)  The  laws  of  refraction. 

I.    The  angles  of  incidence  and  refraction  lie  in  one  plane. 


NOTES   ON   THE   EXPERIMENTS  143 

2.  The  angle  of  refraction  is  smaller  or  larger  than  the 
angle  of  'incidence  -,  according  as  the  light  passes  from  a  rarer 
to  a  denser  medium,  or  the  reverse. 

3.  The  index  of  refraction  has  a  constant  value  for  the 
same  two  media. 

(e)  Some  definitions  : 

I  .    The  index  of  refraction  is  the  ratio  of  the  sine  of  the 
angle  of  incidence  to  the  sine  of  the  angle  of  refraction. 

2.  The  optical  center  of  a  lens  is  a  point  through  which 
a  ray  passes  without  any  appreciable  change  in  direction. 
It  is  frequently  the  geometrical  center  of  the  lens  as  well. 

3.  The  principal  focus  of  a  lens  is  the  point  of  intersec- 
tion of  the  rays  parallel  to  the  principal  axis  after  they 
pass  through  the  lens. 

4.  The  focal  length  of  a  lens  is  the  distance  from  its 
optical  center  to  its  principal  focus. 

5.  A  real  image  is  formed  by  the  actual  intersection  of 
the  light  rays  and  may  be  received  upon  a  screen. 

6.  A  virtual  image  is  formed  by  the  apparent  intersec- 
tion of  the  light  rays  produced  in  such  a  direction  as  to 
cause  them  to  intersect.     Such  an  image  has  no  real  exist- 
ence outside  of  the  eye. 

7.  Conjugate  foci  are  two  points  so  related  to  a  lens  or 
mirror  that  if  a  luminous  point  is  placed  at  one  of  these 
points  its  image  will  be  formed  at  the  other.     It  is  imma- 
terial at  which  point  the  object  is  placed;  its  image  will 
appear  at  the  other. 

8.  A  simple  relation  connecting  the  focal  length  and 
the  distance  from  the  conjugate  foci  to  the  optical  center 
of  a  lens  or  mirror  is  as  follows  : 


where  F  =  the  focal  length  of  the  lens, 


144  PHYSICAL   LABORATORY   GUIDE 

d0  =  the  distance  of  the  object  from  the  optical 

center  of  the  lens, 
di  —  the  distance  from  the  image  to  the  optical 

center  of  the  lens. 

NOTE.  —  In  the  formula  just  given,  the  sign  of  F  is  positive  for  a 
converging  lens  and  negative  when  the  lens  is  diverging. 


SOUND 

(Chapter  IX) 
XXVII.    Sound.— 

(a)  Simple  harmonic  motion,  two  definitions  : 

1.  It  is  a  vibration  in  a  straight  line,  the  motion  being 
such  that  the  vibrating  point  has  an  acceleration  which  is 
toward  the  center  of  its  path  and  proportional  to  its  dis- 
tance from  the  center. 

2.  When  a  body  vibrates  to  and  fro  in  a  straight  line, 
in  such  a  manner  that  its  position  at  any  moment  is  the 
same  as  the  projection  on  that  line  of  a  point   moving 
uniformly  in  a  circle  whose  diameter  is  the  length  of  the 
straight  line,  it  moves  with  what   is  known  as  a  simple 
harmonic  motion. 

(b)  Waves.     All  bodies  emitting  sound  are  in  a  state  of 
vibration  and  have  a  simple  harmonic  motion.      Such  a 
body  will  impart  its  motion  to  any  elastic  material  medium 
surrounding   it,  and   hence  will   produce  waves    in    that 
medium.     Air  is  the  common  medium  for  the  transmission 
of  sound  waves. 

A  wave  is  the  combination  of  at  least  two  motions ; 
namely,  the  simple,  harmonic  motion  of  the  vibrating  par- 
ticles, and  the  onward  uniform  motion  of  the  disturbance 
through  the  medium.  When  these  two  motions  are  at 
right  angles,  the  waves  are  called  transverse.  Longitudi- 


NOTES   ON   THE   EXPERIMENTS  145 

nal  waves  are  produced  when  both  motions  are  in  the 
same  straight  line.  Sound  waves  are  of  this  kind  and 
consist  of  alternate  condensations  and  rarefactions  in  the 
medium.  Each  complete  vibration  of  the  sounding  body, 
that  is,  a  motion  twice  over  its  path,  once  in  each  direction, 
produces  one  wave.  Hence  the  length  of  one  wave  multi- 
plied by  the  number  of  complete  vibrations  made  per 
second  must  give  the  distance  traveled  by  the  sound  in 
one  second,  or  its  velocity.  In  algebraic  form  this  relation 
is  expressed  thus : 

V=LN 

when  V—  the  velocity  of  sound, 

L  =  the  wave  length, 
N  =  the  number  of  vibrations  per  second. 

Experiment  proves  that  sounds  of  different  vibration 
rates,  hence  different  pitches,  all  have  the  same  velocity. 

For  this  reason  equation  (i)  shows  that  the  wave  length 
depends  upon  the  vibration  rate.  The  greater  the  vibra- 
tion rate,  the  shorter  the  wave  length,  and  vice  versa. 

(c)  The  sine  curve.  The  various  vibrating  parts  of  a 
medium  at  different  distances  from  the  source  of  the  dis- 
turbance are  not  in  the  same  phase ;  that  is,  they  do  not 
all  reach  any  particular  point  in  their  path,  such  as  the 
middle  point,  at  the  same  time,  but  each  is  just  a  little 
behind  its  predecessor.  Now,  if  the  different  positions  of 
these  particles  in  their  paths  at  the  same  instant  are  plotted 
as  ordinates  and  the  regular,  even  distance  between  the 
paths  as  abscissae,  the  resulting  wavelike  form  connecting 
these  points  is  called  a  sine  curve. 

Although  these  curves  do  not  show  the  true  form  of  a 
sound  wave  which,  as  stated  above,  is  a  longitudinal  and 
not  a  transverse  vibration,  still  they  throw  much  light  upon 
such  quantities  as  wave  length,  amplitude,  period  of  vibra- 


146  PHYSICAL   LABORATORY   GUIDE 

tion,  resonance,  interference,  and  harmonic  overtones,  and 
therefore  are  a  valuable  part  of  the  student's  work  in  sound. 

(d}  Some  definitions : 

Resonance  is  the  increase  in  the  intensity  of  a  sound 
due  to  two  or 'more  waves  coming  together  in  like  phase, 
and  therefore  producing  a  wave  of  greater  amplitude,  and 
hence  greater  intensity. 

Interference  is  the  decrease  in  the  intensity  of  a  sound 
due  to  two  or  more  waves  coming  together  in  opposite  phase, 
and  hence  producing  a  wave  of  amplitude  equal  to  the  dif- 
ference between  the  amplitudes  of  the  component  waves. 
Sometimes  the  interference  is  complete,  and  silence  results. 

Beats.  Two  trains  of  sound  waves  of  slightly  different 
length  coming  together  in  the  same  medium  will  cause 
alternate  resonance  and  interference  to  take  place.  The 
uneven  volume  of  sound,  or  surging,  as  it  is  sometimes 
called,  thus  produced,  is  known  as  beating. 

Harmonic  overtones  are  tones  of  higher  pitch,  whose 
vibration  rates  are  2,  3,  4,  5,  etc.,  times  as  great  as  the 
fundamental  tone.  Some  of  these  are  usually  present  in 
sounding  bodies,  and  are  due  to  the  vibration  of  the  body 
in  parts  at  the  same  time  that  it  vibrates  as  a  whole. 

The  quality  of  a  sound  depends  upon  the  number  and 
relative  intensity  of  these  harmonic  overtones. 

(e)  The  laws  of  vibrating  strings. 

1 .  The  vibration  rate  of  a  string  varies  inversely  as  the 
length. 

2.  The  vibration  rate  of  a  string  varies  inversely  as  the 
diameter. 

3.  The  vibration  rate  of  a  string  varies  directly  as  the 
square  root  of  the  tension. 

4.  The  vibration  rate  of  a  string  varies  inversely  as  the 
square  root  of  the  density  of  the  material  of  which  it  is  made. 


CHAPTER    XI 


TABLES   OF   PHYSICAL  CONSTANTS 


I.     MENSURATION 

Circle:    radius  =  R;    circumference  =  2  irR;     area       = 
Sphere  :  radius  =  R ;    surface 


=  4  TrR2;    volume  =  f  ?rR3. 


II.    ENGLISH  AND   METRIC  EQUIVALENTS 

LENGTH 
i  inch 
I  centimeter 


2.54  centimeters 
.3937  inch 


I  mile 

I  kilometer 

I  pound 
I  ounce 


MASS 


1.61  kilometers 
.6214  mile 

453-59  grams 
28.35  grams 


III.    BAROMETRIC   CORRECTIONS 

(a)  CORRECTION  FOR  TEMPERATURE 
Mercury  —  Brass  scale  correct  at  o°  C. 


TEMPERATURE 

73 

74 

75 

76 

77 

78 

79 

Degrees  C. 

15 

0.178 

0.181 

0.183 

0.186 

o.i  88 

0.191 

0.193 

16 

0.190 

0.193 

0.196 

0.198 

O.2OI 

0.203 

0.206 

17 

O.2O2 

o  205 

0.208 

O  2IO 

0.213 

0.216 

0.218 

18 

O.2i4 

0.217 

0.220 

0.223 

0.226 

0.229 

0.231 

19 

O.220 

0.229 

0.232 

0-235 

0.238 

0.241 

0.244 

20 

0.238 

0.241 

0.244 

0.247 

0.251 

0.254 

0.257 

21 

0.250 

0.253 

0.256 

0.260 

0.263 

0:267 

0.270 

22 

O.26I 

0.265 

0.269 

0.272 

0.276 

0.279 

0.283 

23 

0.273 

0.277 

0.281 

0.284 

0.288 

0.292 

0.296 

24 

0.285 

0.289 

0.293 

0.297 

0.301 

0.305 

0.309 

Corrections  are  to  be  subtracted  from  observed  readings  —  viz.  if  reading  at 
19  is  76  centimeters,  the  "corrected"  reading  is  76-0.235  =  75.765  centimeters, 


148 


PHYSICAL   LABORATORY   GUIDE 
(b}  CORRECTION  FOR  VARIATION  IN  g. 


LATITUDE 

73 

74 

75 

76 

77 

78 

79 

35°  or  55° 

0.065 

0.066 

0.066 

0.067 

0.068 

0.069 

0.070 

40°  or  50° 

0.032 

0.033 

0.033 

0.034 

0-035 

0.035 

o-°35 

45  5 

o 

o 

o 

0 

0 

o 

0 

(c)  CAPILLARY  DEPRESSION  OF  MERCURY  IN  GLASS 
Height  of  Meniscus  in  Millimeters 


0.4 

0.6 

0.8 

I 

1.2 

1.4 

1.6 

1.8 

Corrections  to  be  Added 

Diameter 
mm. 

4 
5 
6 
7 
8 
9 
10 
11 
12 
13 

mm. 
0.83 
0.47 
0.27 

0.18 

mm. 
1.22 
0.65 
0.41 
0.28 
O.2O 
0.15 

mm. 

0.86 
0.56 
0.40 
0.29 

O.2I 
O.I5 
0.10 

0.07 
0.04 

mm. 
1.98 
I.IO 

0.78 

0-53 
0.38 
0.28 
0.20 
O.I4 
O.IO 
0.07 

mm. 

2-37 

145 
0.98 

0.67 
0.46 

°-33 
0.25 
0.18 
0.13 

O.IO 

mm. 

mm. 

mm. 

1.80 
1.  21 
0.82 
0.56 
0.40 
0.29 
0.21 
O.I5 
O.I  2 

143 
0.97 
0.65 
0.46 

o-33 
0.24 
0.18 

0.13 

M3 

0.77 
0.52 

o.37 
0.27 
0.19 
0.14 

(</)  REDUCTION  OF  BAROMETER  READING  TO  32°  F. 


INCHES 

°F. 

24.0 

24.5 

25.0 

25.5 

26.0 

26.5 

27.0 

27.5 

28.0 

28.5 

29.0 

29.5 

30.0 

30.5 

31.0 

30 

-003 

-.003 

-.003 

-.003 

-.003 

-003 

-.003 

-.003 

-.003 

-.004 

-.004 

-.004 

-.004 

-.004 

-.004 

31 

005 

.005 

.005 

.005 

.006 

.006 

.006 

.006 

.006 

.006 

.006    .006 

.006 

.007 

.007 

32 

.007 

.008 

.008 

.008 

.co8 

.008 

.008 

.008 

.009 

.009 

.009]  .009 

.009 

.009 

.009 

33 

.010 

.010 

.010 

.010 

.010 

.010 

.Oil 

.on 

.on 

.Oil 

.012 

.012 

.012 

.012 

.012 

34 

.012 

.012 

.012 

.012 

.013 

.013 

.013 

.013 

.014 

.014 

.014 

.014 

.015 

.015 

.015 

35 

.014 

.014 

.014 

.015 

.015 

.015 

.016 

.016 

.016 

.016 

.017 

.017 

.017 

.018 

.018 

36 

.016 

.Ol6 

.017 

.017 

.017 

.018 

.018 

.018 

.019 

.019 

.019 

.020 

.020 

.020 

.O2I 

37 

.Ol8 

.019 

.QIC 

.019 

.020 

.020 

.021 

.021 

.021 

.022 

.022       .022 

.023       .023 

.024 

38 

.020 

.021 

.021 

.022 

.022 

.022 

.023 

.023 

.024 

.024 

.025 

.025 

.O26|     .026 

.026 

39 

.023 

.023 

.024 

.024 

.024 

.025 

.025 

.026 

.026 

.027 

.027 

.0^8 

.028 

.029 

.029 

40 

.025 

.025 

.026 

.026 

.027 

.027 

.028 

.028 

.029 

.030 

.030 

.030 

.031 

.031 

.032 

41 

.027 

.027 

.028 

.02^ 

.029 

.030 

.030 

.031 

.031 

.032 

•033 

•°33 

•034 

•034 

•035 

42 

.029 

.030 

.030 

.031 

.032 

.032 

•033 

•°33 

•034 

•034 

•035 

.036 

.036       .037 

.038 

43 

.031 

.032 

•03? 

•°33 

•034 

•°35 

•035 

.036 

.036 

•037 

.038 

.038 

.039       .040 

.040 

44 

•033 

.034 

•035 

•035 

.036 

•037 

.038 

.038 

•039 

.040 

.040 

.041 

.042 

.042 

•°43 

TABLES    OF    PHYSICAL    CONSTANTS 


149 


(</)  REDUCTION  OF  BAROMETER  READING  TO  32°  F.  —  Continued 


1 

I 

NCHES 

24.0 

24.5 

25.0 

25.5 

26.0 

26.5 

27.0 

27.5 

28.0 

28.5 

29.0 

29.5 

30.0 

30.5 

31.0 

45 

-.036 

-•°37 

-•°37 

-.038 

-•°39 

-•°39 

-.040 

-.041 

-.042 

-.042 

-043 

-.044 

-045 

-•045 

-.046 

46 

.038 

.038 

•°39 

.040 

.041 

.042 

•°43 

•°43 

.044 

•°45 

.046 

.046 

.047 

.048 

.049 

47 

.040 

.041 

.041 

.042 

•043 

.044 

•045 

.046 

.047 

.048 

.048 

.049 

.050 

.051 

.052 

4s; 

.042 

•043 

.044 

•«45 

.046 

.047 

.047 

.048 

.049 

.050 

.051 

.052 

•053 

•053 

•°54 

49 

.044 

•°45 

.046 

.047 

.048 

.049 

.050 

.051 

•052 

.052 

•054 

•054 

•055 

•056 

•°57 

50 

046 

.047 

.048 

.049 

.050 

.051 

.052 

•053 

•°54 

•055 

.056 

•057 

.058 

•059 

.060 

51 

.049 

.050 

.051 

.052 

•°53 

•054 

•055 

.056 

•057 

.058 

•°59 

.060 

.061 

.062 

.063 

52 

•051 

.052 

•053 

•054 

•055 

.056 

•°57 

.058 

•059 

.060 

.061 

.062 

.064 

.065 

.066 

53 

•053 

•054 

•055 

.056 

•057 

.058 

.060 

.061 

.062 

.063 

.064 

.065 

.066 

.067 

.068 

54 

•055 

.056 

•057 

.058 

.060 

.061 

.062 

.063 

.064 

.065 

.067 

.068 

.069 

.070 

.071 

55 

•057 

.058 

.060 

.061 

.062 

.063 

.064 

.065 

.066 

.068 

.069 

.070 

.071 

•073 

.074 

56, 

.060 

.061 

.062 

.063 

.064 

.065 

.067 

.068 

.069 

.070 

.072 

•°73 

.074 

•075 

.077 

57 

.062 

.063 

.064 

.065 

.067 

.068 

.069 

.070 

.072 

•°73 

•075 

.076 

.077 

.078 

.080 

58, 

.064 

.06=; 

.066 

.068 

.069 

.070 

.071 

•°73 

.074 

.076 

.077 

.078 

.080 

.081 

.082 

59 

.066 

.068 

.069 

.070 

.072 

•073 

.074 

•°75 

.077 

.078 

.080 

.081 

.083 

.084 

.085 

60 

.068 

.070 

.071 

.072 

.074 

.076 

.077 

.078 

.079 

.081 

.082 

.084 

.085 

.086 

.088 

61 

.070 

.072 

•073 

.074 

.076 

.077 

.079 

.080 

.082 

.083 

.085 

.086 

.088 

.089 

.091 

62 

•073 

.074 

.076 

.077 

.079 

.080 

.082 

.083 

.085 

.086 

.088 

.089 

.091 

.092 

.094 

63 

•075 

.076 

.078 

.079 

.081 

.082 

.084 

.085 

.087 

.088 

.090 

.091 

•093 

•°95 

.096 

64 

.077 

.078 

.080 

.081 

.083 

.085 

.086 

.088 

.090 

.091 

•093 

.094 

.096 

.097 

.099 

65 

.079 

.080 

.082 

.084 

.086 

.087 

.089 

.090 

.092 

•093 

•°95 

.097 

.099 

.100 

.102 

66 

.081 

.083 

.085 

.086 

.088 

.089 

.091 

•°93 

•095 

.096 

.098 

.099 

.101 

.103 

.IO5 

67; 

.083 

.085 

.087 

.088 

.090 

.092 

.094 

•°95 

.097 

.099 

.101 

.102 

.104 

.106 

.108 

68 

.085 

.087 

.089 

.090 

•°93 

.094 

.096 

.098 

.100 

.101 

.103 

.105 

.107 

.108 

.IIO 

69 

.088 

.089 

.091 

•093 

•095 

.097 

.099 

.100 

.102 

.104 

.106 

.107 

.110 

.in 

•"3 

70 
71 

.090 

.092 

.094 

.096 
.008 

.097 

.099 

.101 

.103 

.105 

.106 

.109 

.110 

.112 

.114 

.116 

1  TO 

72 

.092 
.094 

.094 
.096 

.098 

.100 

.102 

.104 

.106 

.108 

.IIO 

.112 

.114 

.116 

.118 

.120 

.  i  iy 
.122 

73 

.096 

.098 

.100 

.102 

.104 

.106 

.108 

.110 

.TI2 

.114 

.116 

.118 

.I2O 

.122 

.124 

74 

.098 

.100 

.103 

.105 

.107 

.109 

.in 

.113 

.115 

.117 

.119 

.121 

.123 

•125 

.127 

75 

.101 

.102 

.105 

.106 

.log 

.in 

•  "3 

•  "5 

.117 

.119 

.122 

.124 

.126 

.128 

.130 

76 

.103 

.104 

.107 

.I09 

.III 

.113 

.116 

.118 

.120 

.122 

.124 

.126 

.128 

.130 

•133 

77 

.105 

.107 

.109 

.III 

.114 

.116 

.118 

.120 

.122 

.124 

.127 

.129 

.131 

•133 

.136 

78 

.107 

.109 

.112 

.113 

.116 

.118 

.120 

.122 

.125 

.127 

.129 

.131 

.134 

.136 

.138 

79 

.109 

.III 

.114 

.Il6 

.118 

.120 

.123 

.125 

.127 

.129 

,I32 

•134 

•137 

•139 

.141 

80 

.in 

.113 

.116 

.118 

.121 

.123 

•125 

.127 

.130 

.132 

•  !35 

•T37 

•139 

.141 

.144 

81 

.114 

.Il6 

.118 

.I2O 

.123 

.125 

.128 

.130 

.132 

•134 

•137 

•139 

.142 

•144 

.147 

82 

.116 

.118 

.121 

.122 

.125 

.128 

.130 

.132 

.140 

.142 

•145 

.147 

.149 

83 

.118 

.120 

.123 

•  125 

.128 

.130 

•133 

•135 

'.138 

.140 

.142 

•145 

.147 

.149 

.152 

84 

.120 

.122 

.125 

.127 

.130 

.132 

•135 

.138 

.140 

.142 

•145 

.147 

.ISO 

•152 

•155 

85 

.122 

.124 

.I27 

.129 

.132 

•134 

•137 

•139 

•143 

•145 

.148 

.150 

•153 

•155 

'III 

86 

.124 

.126 

.128 

.130 

•135 

.140 

•143 

•145 

.I48 

.150 

•155 

.158 

87 
8£ 

.126 

.129 

.132 

•134 

•137 

•139 

.142 

.144 

.148 

.150 

•153 

•'55 

.158 

'  tf\1 

!i63 
1  66 

89 

'.13? 

[133 

.136 

•139 

.142 

.144 

•147 

•  ISO 

.153 

•155 

.158 

.161 

.l64 

.103 
.166 

!x6g 

90 

•133 

.136 

.138 

.141 

.144 

.147 

•  ISO 

.I53 

•155 

•157 

.161 

.164 

.166 

.I69 

.172 

91 

•135 

.138 

.141 

•143 

.146 

.149 

.152 

.155 

.158 

.160 

.163 

.166 

.169 

.172 

.175 

92 
93 

•137 
•139 

.140 
.142 

•143 
•145 

.146 
.148 

.149 

.152 
•154 

•154 
•157 

•J57 
.160 

.160 
.163 

.163 
.166 

.166 
.168 

.169 
.171 

.172 
.174 

•175 
.177 

.177 
.180 

94 

.142 

•  145 

.147 

.150 

•153 

.156 

•159 

.162 

.165 

.168 

.171 

.174 

.177 

.ISO 

•183 

95 

.144 

.147 

.150 

•T53 

.156 

•159 

.162 

.165 

.168 

.171 

.174 

.177 

.ISO 

i?3 

.186 

96 

.146 

.149 

.152 

•  155 

.161 

.164 

.167 

.170 

•173 

.176 

.179 

.182 

ix85 

.188 

97 

.148 

•IS1 

•154 

•J57 

.160 

.164 

.167 

.170 

•173 

.176 

.179 

.182 

.185 

.188 

.191 

98 

.150 

•153 

.156 

.160 

.163 

.166 

.169 

.172 

•T75 

.178 

.181 

.185 

.188 

.191 

.194 

99 

.152 

•J55 

•159 

.162 

•165 

.168 

.171 

•175 

.178 

.l8l 

.184 

.187 

.190 

.194 

.197 

100 

•154 

•157 

.161 

.164 

.l67 

.171 

.174 

.177 

.183 

.l84 

.187 

.190 

•193 

.197 

.200 

ISO 


PHYSICAL   LABORATORY   GUIDE 


IV.     DENSITIES 

# )  DENSITIES  —  MISCELLANEOUS 


GRAMS  PER  CUBIC 
CENTIMETER 

POUNDS  PER  CUBIC 
FOOT 

Agate  

2.S   —2.7 

156-168 

'J          I 
I.OO-I.II 

66-  69 

Anthracite  coal      .     .          .          . 

1.4.  -I  8 

87-112 

Asbestos  

2.0   -2.8 

I2C,—  I7C 

I.I    -1.2 

6q-  7"; 

Beeswax  .     .          . 

.q6-   .07 

60-  61 

Bone   

1.7  —  2.O 

106—125 

2.6 

162 

Brick                            .          .... 

2.O  —2.2 

I2C-I37 

Butter      

.86-  .87 

CT—   1:4. 

Caoutchouc  
Cement  set                      .               .     . 

.92-  .99 
27—10 

57-  62 
168-187 

Chalk  

1.9  -2.8 

1  18—171; 

.28-  .157 

I7.C-   T.C 

Cherry  wood 

70—    qo 

4.3—  ^6 

Coal,  soft      

1.2  —IX 

7c—  q4 

Coke    

I.O  —1.7 

/5    v^- 
62-105 

Cork 

' 

22—     26 

14—  1  6 

Corundum         .     .          .     .          . 

•3  Q   —  4.0 

24.i;-2^O 

Diamond      

5'V      *** 

3.c  —  3.6 

220-225 

Kmery 

A   O 

2  CQ 

Flint                   

261 

164 

Fluorspar      

•2.14-7.18 

iq6—  iq8 

Galena 

77     76 

4.60-470 

Gas  carbon                       .               . 

i  88 

I  iq 

Glass,  common       

2.4   -2.8 

I  ^0-171; 

Glass,  flint    

2.q  —  4.? 

180-280 

Glue 

I  27 

80 

Granite         

2.C    -I.O 

IC6-I87 

I.Q   —2.3 

120-140 

Ice      

.88-  .91 

cr-    1:7 

Iodine      

4.  q^ 

3OQ 

Ivory  

I.53—I.Q2 

II4—I2O 

Kaolin 

2  2 

I  37 

Lime,  Quick      

2-2—72 

144—  2OO 

Lime,  slaked     

1.3  —1.4. 

81-  87 

1.65-1.78 

103—1  1  1 

Limestone                   .               .     . 

2  46-2  86 

I  C4—  I  78 

Lignum  vitae     

I  17—  I  33 

73-   83 

Maple      

.62—  .7C 

TO_  47 

Marble     

2.5  -2.8 

I  C7-I77 

Masonry       

I  8^-2  3 

1  1  6—  1  4.4. 

Mica    

';;•>      'J 

2.6  —3.2 

165—200 

Oak                    .     . 

60—   90 

37—    ^5 

o/       0^ 

TABLES    OF   PHYSICAL   CONSTANTS 

«     DENSITIES  —  MISCELLANEOUS.  —  Continued 


GRAMS  PER  CUBIC 
CENTIMETER 

POUNDS  PER  CUBIC 
FOOT 

Paper                                   .     . 

0.  7  —  1  .  1  C 

44—  72 

Paraffin    

.87-  .01 

C4-    ry 

Peat                                    ... 

.84 

C2 

1.82 

1  14 

Pitch  

1.07 

67 

Porcelain                          ...          . 

2.1   —  2.S 

' 
14-1-1  e6 

Pyrites     

4.Q   -5.2 

'106—324 

•  37—   .QO 

•  2v;6 

Quartz 

'ji      *y 
2.6* 

03" 

i6c 

Resin  .          

1.07 

J  • 
67 

Rock  salt      

2.28-2.41 

142—150 

Sal  ammoniac                   . 

I.e   -1.6 

Q4—  IOO 

Saltpeter            .          

1.95-2.08 

I22-I3O 

1.40—  i.  6c 

87—IO3 

Sand    damp                            . 

I  QO—  2  OS 

1  19—128 

Sandstone                    .          .... 

2.2   -2.5 

137—  1<\6 

Shale  

2.6 

l62 

2.O  -2.<: 

125-156 

Slate                        

2.6   —2.7 

162-168 

Snow,  loose       

.I2C 

7.8 

Starch      
Suffar 

1.53 

i  61 

95 

IOO 

Talc    .     

2.7 

1  68 

Tallow     

.01—  .Q7 

<I7—  60.  C 

Trap  rock               

•y*      -yj 

26—27 

162—170 

Walnut    

.64-  .70 

4O-  43 

Willow 

•™     •/ 

40—    60 

24—    37 

DENSITIES  OF  METALS 


GRAMS  PER  CUBIC 
CENTIMETER 

POUNDS  PER  CUBIC 
FOOT 

Aluminum   cast 

2  56-  2  58 

160—  161 

Aluminum,  wrought  .     .          . 

2  65—   2  80 

l6c—  I7C 

Antimony,  solid    

6.7  —  6  72 

*"j  *o 

4l8—  4IQ 

6.22 

Bismuth  solid            . 

Q  67 

6OA 

Bismuth,  liquid           .          .... 

10  004 

624 

Copper,  cast     

8.80-  S.QI; 

"•"r 

C4Q—  cc8 

Copper,  wrought 

ggt     SQI; 

CC2    CC8 

JJ-6  DJ" 

PHYS.  LAB.  GUIDE  —  1 1 


152 


PHYSICAL   LABORATORY    GUIDE 

(b)  DENSITIES  OF  METALS.  —  Continued 


GRAMS  PER  CUBIC 
CENTIMETER 

POUNDS  PER  CUBIC 
FOOT 

822 

r  f  •? 

Gold                                            .     .     . 

IQ.T?—  IQ    -1* 

D1  J 

1  2O7 

Iron   gray  cast  

7.O7-    7.1^ 

A  70—4.4.  C 

7  80—    7  QO 

48?    AQ^ 

Iron   liquid                  . 

688 

42Q 

Lead,  cast          

11.34 

708 

Lead,  wrought  

^7 

I  I.  36 

7OQ 

10  65 

664 

Mercury             .                     ... 

i  '\  ^06 

848 

Nickel      .                

8.3  -  8.Q 

ci7-ccc 

21  2   —21  7 

1322    13^4 

Silver   cast             .          

IO  4   -IO  C 

640—  6  c  c 

Silver,  wrought      

IO.CS—  IO.C7 

6q8-6i;q 

Q  ? 

CO'? 

Tin   cast 

7  2Q 

3yj 

ACC 

Tin,  wrought    

7.  3O 

4.cc 

Tin,  liquid    

698 

4iiD 
4^6 

7  04—  7  1  6 

4^Q—  447 

7.IQ 

440 

Zinc,  liquid  .     .     .     . 

6.48 

4O4 

DENSITIES  AND  COMPOSITIONS  OF  ALLOYS 


GRAMS  PER 
CUBIC 

CENTIMETER 

POUNDS  PER 
CUBIC  FOOT 

Brasses,  yellow,  cast 

70  Cu  +  3O  Zn  .     .     . 

8-44 

527 

Brasses,  yellow,  rolled 

. 

8.56 

534 

Brasses,  yellow,  drawn 

. 

8.7 

542 

Brasses,  red 

90  Cu+io  Zn  .     .     . 

8.6 

536 

Brasses,  white 

50  Cu+5O  Zn  .     .     . 

8.2 

511 

Bronzes 

90  Cu-f-io  Sn  .     .     . 

8.78 

548 

Bronzes 

80  Cu+20  Sn  .     .     . 

8.74 

545 

German  silver,  Berlin  (i) 

52Cu  +  26Zn  +  22Ni 

845 

527 

German  silver,  Berlin  (2) 

59  Cu-f  3Q,Zn+  1  1  Ni 

8-34 

520 

German  silver,  Berlin  (3) 

6.iCu  +  3oZn-f  6Ni 

8.30 

518 

German  silver 

Nickelin                  . 

8.77 

1:47 

Wood's  metal 

50  Bi  +  25  Pb  +  12.5 

/  / 

D  '  / 

Cd  +  i2.5Sn     .     . 

9.70 

605 

TABLES   OF    PHYSICAL    CONSTANTS 
(X)  DENSITIES  OF  LIQUIDS 


153 


GRAMS  PER  CUBIC 
CENTIMETER 

POUNDS  PER 
CUBIC  Poor 

Alcohol,  ethyl,     absolute 

C. 

15°      .... 

•794 

494 

Alcohol,  ethyl,     95  % 

15'      .... 

.808 

5°4 

Alcohol,  ethyl,     90  % 

15°      .... 

.823 

51.2 

Alcohol,  ethyl,     85  % 

15°      .... 

.836 

5*-9 

Alcohol,  methyl,  absolute 

15°      .... 

.796 

49-5 

Alcohol,  methyl,  95  % 

15°      .... 

.810 

5°-5 

Alcohol,  methyl,  90  % 

I5°      .... 

.823 

51-2 

Alcohol,  methyl,  85  % 
Carbon  disulphide 

15°      .... 

15°      .... 

•837 
1.293 

8cx6 

Ether 

0°        .... 

.736 

45-9 

Glycerine 

0°        .... 

1.26 

78.6 

Mercury  (quicksilver) 

0°        .... 

I3-596 

836. 

Oil,  castor 

15°   .... 

.969 

60.5 

Oil,  linseed,  boiled 

15°  .... 

.942 

58.8 

Oil,  olive 

15°  .... 

.918 

57-3 

Oil,  turpentine 

15°  .... 

.873 

54-2 

Oil,  petroleum 

0°        .... 

.878 

54-8 

Oil,  gasoline 

. 

.629-.667 

39-2 

Oil,  kerosene 

. 

.807 

5°-3 

Sea  water 

15°  .... 

1.025 

64. 

(<?)  DENSITIES  OF  GASES. — AT  oc  C.  AND  760  MM. 


GRAMS  PER  CUBIC 
CENTIMETER 

POUNDS  PER 
CUBIC  FOOT 

Air  

.OOI2Q7. 

0807 

.00  1  q  74. 

1272 

Hydrogen 

00009 

•A^J^ 

ooco 

Oxvcren 

0014 

0807 

Steam,  at  100°  C  

00058 

0763 

154  PHYSICAL   LABORATORY   GUIDE 

(/)  DENSITY  OF  WATER  AT  DIFFERENT  TEMPERATURES 


DEGREES  C. 

GRAMS  PER  CUBIC 
CENTIMETER 

DEGREES  C. 

GRAMS  PER  CUBIC 
CENTIMETER 

0 

0.999878 

16 

0.999004 

1 

0-999933 

17 

0.998839 

2 

0.999972 

18 

0.998663 

3 

0.999993 

19 

0.998475 

4 

I.OOOOOO 

20 

0.998272 

5 

0.999992 

21 

0.998065 

6 

0.999969 

22 

0.997849 

7 

0.999933 

23 

0.997623 

8 

0.999882 

24 

0.997386 

9 

0.999819 

25 

0.097140 

10 

0.999739 

26 

0.99686 

11 

0.999650 

27 

0.99659 

12 

0.999544 

28 

0.99632 

13 

0.999430 

29 

0.99600 

14 

0.999297 

30 

0-99577 

15 

0.999-54 

31 

0-99547 

V.    E.  M.  F.  OF   COMMON  CELLS 


NAME 

E.  M.  F. 

0.98  volt 

Daniell  (zinc,  acid,  copper  sulphate,  copper)  ...» 

1.09  volts 
1  .8    volts 

1.86  volts 

Chromate  (zinc,  acid,  chromic  acid,  carbon)   .... 
LeClanche      .....          

2       volts 
1.46  volts 

0.70  volt 

Dry-cell      '.     .     .     . 

1.3    volts 

I.  O2  volts 

VI.    *  ELECTROCHEMICAL  EQUIVALENTS 


Chlorine    .     . 
Copper,  cupric 
Hydrogen 
Iron,  ferric     . 


.0003675 
.0003271 
.000010352 
.0001932 


Oxygen 0000828 

Silver 0011180 

Zinc 000338 


*  Grams  deposited  by  one  ampere  per  second. 


TABLES   OF   PHYSICAL   CONSTANTS 


155 


VII.    COEFFICIENTS  OF  EXPANSION  BETWEEN  0°  AND  100°  C. 

« 
LINEAR 


Aluminum     ....  0.00002221 

Antimony      ....  0.00000980 

Bismuth    .....  0.00001330 

Brass 0.00001875 

Bronze 0.00001844 

Copper 0.00001866 

Ebonite 0.00008420 

Glass,  tube    ....  0.00000833 

Glass,  rod      ....  0.00000861 

Gold 0.00001460 

Graphite 0.00000786 

Iron,  cast 0.00001125 

Iron,  wrought    .     .     .  0.00001220 


Lead 0.00002799 

Marble 0.00000786 

Paraffin 0.00027854 

Pine 0.00000496 

Platinum 0.00000886 

Sandstone,  red  .     .     .  0.00001174 

Silver 0.00001943 

Sulphur 0.00006413 

Steel,  tempered.     .     .  0.00001322 

Steel,  untempered .     .  0.00001095 

Tin 0.00002296 

Zinc 0.00002976 


VIII.    ACCELERATIONS  DUE  TO   GRAVITY 


latitude  52°  30' 981.25  cm.  per  (sec.)2 

latitude  51°  29' 981.17  cm.  per  (sec.)'2 

latitude  48°  50' 980.94  cm.  per  (sec.)2 

latitude  40°  43' 980.19  cm.  per  (sec.)2 

Washington,  latitude  38°  54' 980.06  cm.  per  (sec.)2 

Latitude            45° 980.61  cm.  per  (sec.)2 

Equator 978.10  cm.  per  (sec.)2 

Pole .  983.11  cm.  per  (sec.)2 


Berlin, 

Greenwich, 

Paris, 

New  York, 


IX.    LENGTH   OF   SECONDS  PENDULUM 


Greenwich,  latitude  51°  29'  .  .' 99.413  cm. 

Paris,  latitude  48°  50' 99-39O  cm. 

New  York,  latitude  40°  43' .  99.317  cm. 

Washington,  latitude  38°  54' 99.306  cm. 

Latitude  45°  oo' 99-356  cm. 

Equator 99'i°3  cm. 

Pole 99.610  cm. 


1 56 


PHYSICAL   LABORATORY   GUIDE 


X.     TEMPERATURE   OF  THE  DEW  POINT,   IN  DEGREES 
FAHRENHEIT 


1 

DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (t-f) 

| 

(3 

0.5° 

1.0° 

1.5° 

2.0° 

2.5° 

3.0° 

3.5° 

4.0° 

4.5° 

1 
5.0° 

5.5° 

6.0° 

Bl 

Q 

20 

18 

17 

15 

!3 

10 

8 

5 

2 

—  —  2 

-6 

—  12 

—  19 

20 

21 

19 

18 

16 

12 

9 

7 

4 

o 

-4 

-  8 

—  15 

21 

22 

20 

19 

17 

15 

*3 

ii 

8 

6 

—  2 

-  6 

—  ii 

22 

23 

22 

20 

18 

16 

H 

12 

10 

7 

4 

-i 

—   "3 

g 

23 

24 

23 

21 

19 

18 

16 

14 

ii 

9 

6 

3 

~  l 

—  5 

24 

25 

24 

22 

21 

19 

17 

15 

13 

ii 

8 

5 

—  2 

2 

25 

26 
27 

3 

23 
24 

22 
23 

20 
21 

18 
20 

16 

18 

14 
16 

12 

14 

10 
ii 

7 
9 

6 

O 

26 
27 

28 

27 

24 

22 

21 

19 

17 

15 

13 

ii 

8 

c 

28 

29 

28 

26 

25 

24 

22 

20 

19 

H 

12 

10 

7 

29 

30 

29 

27 

26 

25 

23 

22 

20 

18 

16 

H 

ii 

9 

30 

31 

3° 

29 

27 

26 

24 

23 

21 

19 

18 

15 

13 

ii 

31 

32 

31 

3° 

28 

27 

26 

24 

22 

21 

19 

15 

13 

32 

33 

31 

29 

28 

26 

25 

23 

22 

19 

18 

16 

i^ 

33 

34 

32 

32 

3° 

29 

27 

26 

24 

24 

21 

20 

18 

16 

34 

35 

33 

32 

3i 

3° 

29 

28 

26 

25 

23 

22 

20 

18 

35 

36 

35 

34 

32 

30 

29 

27 

26 

24 

23 

21 

19 

36 

37 

36 

35 

33 

32 

31 

30 

28 

27 

26 

24 

22 

21 

37 

38 

37 

36 

34 

33 

32 

31 

3° 

28 

27 

26 

24 

22 

38 

39 

38 

37 

35 

34 

33 

32 

30 

29 

28 

27 

25 

24 

39 

40 

39 

38 

36 

35 

34 

33 

3, 

30 

29 

28 

26 

25 

40 

41 

40 

39 

37 

36 

•35 

34 

32 

22 

3° 

29 

28 

26 

41 

42 

40 

39 

38 

36 

35 

34 

33 

31 

3° 

29 

27 

42 

43 

42 

40 

39 

37 

36 

35 

34 

32 

30 

29 

43 

44 

43 

42 

4i 

40 

38 

37 

36 

35 

33 

32 

31 

30 

44 

45 

44 

43 

42 

4i 

40 

39 

37 

36 

34 

33 

32 

3 

45 

46 

45 

44 

43 

42 

41 

40 

38 

37 

36 

35 

33 

32 

46 

47 

46 

45 

44 

43 

42 

•40 

39 

37 

36 

34 

33 

47 

48 
49 

3 

46 
47 

46 

44 
45 

43 

44 

42 
43 

41 
42 

40 

38 
39 

37 
38 

36 
37 

35 
36 

48 
49 

t 

0.5° 

1.0° 

1.5° 

2.0° 

2.5° 

3.0° 

3.5° 

4.0° 

4.5° 

5.0° 

5.5° 

6.0° 

t 

TABLES   OF   PHYSICAL   CONSTANTS 


157 


X.     TEMPERATURE   OF  THE  DEW   POINT,  IN  DEGREES 
FAHRENHEIT.  —  Continued 


d 

DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (t-f) 

| 

•to  H 
P 

0.5° 

1.0° 

1.5° 

2.0° 

2.5° 

3.0° 

3.5° 

4.0° 

4.5° 

5.0° 

5.5° 

6.0° 

1 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

38 

37 

50 

51 

5° 

49 

48 

47 

46 

45 

44 

43 

42 

41 

39 

38 

51 

52 

5° 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

52 

53 

52 

51 

50 

49 

48 

47 

46 

45 

44 

43 

42 

41 

53 

54 

53. 

S2 

51 

50 

5° 

49 

47 

46 

45 

44 

43 

42 

54 

55 

54 

53 

53 

52 

51 

50 

49 

48 

47 

46 

44 

43 

55 

56 

55 

54 

54 

53 

52 

50 

49 

48 

47 

45 

44 

56 

57 

56 

55 

55 

54 

53 

52 

5° 

49 

48 

47 

46 

57 

58 

57 

56 

56 

55 

54 

53 

S2 

51 

5° 

49 

48 

47 

58 

59 

58 

57 

57 

56 

55 

54 

53 

52 

5° 

49 

48 

59 

60 
61 

IS 

58 
59 

58 
59 

1 

56 
57 

1 

54 

55 

53 
54 

53 

52 

50 

49 
50 

60 
61 

62 

61 

60 

60 

58 

56 

55 

54 

53 

S2 

52 

62 

63 

62 

6l 

61 

60 

59 

58 

57 

56 

55 

55 

54 

53 

63 

64 

63 

62 

62 

61 

60 

59 

58 

57 

56 

56 

55 

54 

64 

65 
66 

64 
65 

63 
64 

63 
64 

62 
63 

61 
62 

60 
61 

8 

g 

58 
59 

H 

56 

57 

li 

65 
66 

67 

66 

65 

64 

63 

62 

61 

61 

60 

59 

58 

57 

67 

68 

68 

67 

66 

65 

64 

63 

62 

62 

61 

60 

59 

58 

68 

69 

69 

68 

67 

66 

65 

64 

63 

63 

62 

61 

60 

59 

69 

70 

7° 

69 

68 

67 

67 

66 

65 

64 

63 

62 

61 

61 

70 

71 

71 

7° 

69 

68 

68 

67 

66 

65 

64 

63 

62 

62 

71 

72 

72 

70 

69 

69 

68 

67 

66 

65 

64 

63 

63 

72 

73 

74 

73 
74 

72 
73 

71 

72 

70 
71 

70 
71 

69 

7° 

68 
69 

II 

66 
67 

66 
67 

a 

64 
65 

73 

74 

75 

75 

74 

73 

72 

72 

71 

70 

69 

68 

68 

67 

66 

75 

76 

76 

75 

74 

73 

73 

72 

71 

7° 

69 

69 

68 

67 

76 

77 

77 

76 

75 

74 

74 

73 

72 

70 

70 

69 

68 

77 

78 

78 

77 

76 

75 

75 

74 

73 

72 

71 

71 

70 

69 

78 

79 

79 

78 

77 

76 

76 

75 

74 

73 

72 

72 

71 

70 

79 

80 

80 

79 

78 

77 

77 

76 

75 

74 

73 

73 

72 

72 

80 

t 

05° 

1.0° 

1.5° 

2.0° 

2.5° 

3.0° 

3.5° 

4.0° 

4.5° 

5.0° 

5.5° 

6.0° 

* 

i 

1 

158 


PHYSICAL    LABORATORY   GUIDE 


X.    TEMPERATURE   OF  THE  DEW  POINT,  IN  DEGREES 
FAHRENHEIT.  — Continued 


a 
^ 

1 

DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (t-t') 

| 

J 

>H 
• 

P 

6.0° 

6.5° 

7.0° 

7.5° 

8.0° 

8.5° 

9.0° 

9.5° 

10.0° 

105° 

11.0° 

11.5° 

12.0° 

19 

-25 

19 

20 

-19 

-32 

20 

21 

-15 

-24 

-47 

21 

22 

—  ii 

-19 

-3i 

22 

23 

-  8 

-«4 

-24 

—45 

23 

24 

-  5 

—  10 

-18 

-3° 

24 

25 

—  2 

—  7 

-13 

-42 

25 

26 

O 

—  4 

-  9 

-17 

-28 

26 

27 

-  3 

—  i 

-  6 

—  12 

—  20 

-37 

27 

28 

5 

—  i 

-  3 

-  8 

-15 

-25 

-54 

28 

29 

7 

4 

0 

—  A 

—  10 

-18 

-32 

29 

30 

9 

6 

—  2 

—  2 

-  6 

-'3 

—  22 

-43 

30 

31 

ii 

8 

5 

—  I 

-  3 

-  8 

-15 

-27 

31 

32 

*3 

10 

7 

4 

0 

—  4 

—  10 

-18 

—  33 

32 

33 

M 

12 

9 

6 

-  3 

—  i 

—  6 

—  12 

—  22 

-44 

33 

34 

16 

14 

ii 

8 

6 

—  2 

—  —  2 

-  8 

—  15 

—  27 

34 

35 

18 

15 

U 

10 

8 

5 

—  i 

—  4 

—  9 

—  18 

-32 

35 

36 

19 

'7 

15 

12 

10 

8 

4 

0 

—  r 

—  12 

—  20 

-42 

36 

37 

21 

19 

*7 

14 

12 

9 

6 

-  3 

_  2 

-  6 

—  14 

-25 

p  2 

37 

38 

22 

20 

19 

16 

14 

ii 

9 

6 

—  2 

—  2 

-  8 

—  16 

—29 

38 

39 

24 

22 

20 

18 

16 

H 

ii 

8 

C 

—  I 

-  4 

—  10 

-18 

39 

40 

25 

23 

22 

20 

18 

16 

13 

ii 

8 

4 

0 

-  5 

—  12 

40 

41 

26 

25 

23 

21 

20 

17 

15 

13 

10 

7 

-  4 

—  i 

—  6 

41 

42 

27 

26 

24 

23 

21 

19 

18 

15 

1  2 

10 

7 

-  3 

—  2 

42 

43 

29 

27 

26 

24 

23 

21 

19 

17 

14 

12 

9 

6 

—  2 

43 

44 

3° 

28 

27 

26 

24 

22 

20 

18 

26 

14 

12 

9 

6 

44 

45 

31 

3° 

28 

27 

25 

24 

22 

20 

18 

16 

13 

ii 

8 

45 

46 

32 

3i 

3° 

28 

27 

25 

24 

22 

20 

18 

16 

13 

ii 

46 

47 

33 

32 

3i 

29 

28 

26 

25 

23 

22 

20 

18 

15 

13 

47 

48 

35 

33 

32 

3° 

29 

28 

26 

25 

23 

21 

20 

17 

15 

48 

49 

36 

34 

33 

32 

31 

29 

28 

26 

25 

23 

21 

19 

17 

49 

t 

6.0° 

6.5° 

7.0° 

7.5° 

8.0° 

8.5° 

9.0° 

9.5° 

10.0°  10  5° 

Ii 

11.0° 

11.5° 

12.0° 

t 

TABLES   OF   PHYSICAL   CONSTANTS 


159 


X.     TEMPERATURE   OF  THE  DEW  POINT,  IN  DEGREES 
FAHRENHEIT.  -  Continued 


(I 

DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (/-/') 

jjj 

01 

c 

6.0° 

6.5° 

7.0° 

7.5° 

8.0° 

8.5° 

9.0° 

9.5° 

10.0° 

10.5° 

11.0° 

11.5° 

12.0° 

Q 

50 

37 

35 

34 

33 

32 

31 

29 

28 

26 

24 

23 

21 

19 

50 

51 

38 

37 

36 

34 

33 

32 

31 

29 

28 

26 

24 

22 

21 

51 

52 

40 

38 

37 

36 

34 

33 

32 

-30 

29 

28 

26 

24 

23 

52 

53 

39 

38 

37 

36 

34 

33 

32 

3° 

29 

28 

26 

24 

53 

54 

42 

41 

40 

39 

37 

36 

34 

33 

32 

30 

29 

27 

26 

54 

55 

43 

42 

4i 

40 

39 

37 

36 

34 

33 

32 

30 

29 

28 

55 

56 

44 

43 

42 

41 

40 

39 

37 

36 

34 

33 

32 

30 

29 

56 

57 

46 

45 

44 

42 

40 

39 

37 

36 

35 

33 

32 

30 

57 

58 

47 

46 

45 

44 

42 

41 

40 

39 

37 

36 

35 

33 

32 

58 

59 

48 

47 

46 

45 

44 

43 

4i 

40 

39 

38 

36 

35 

33 

59 

60 

49 

48 

47 

46 

45 

44 

43 

4i 

40 

39 

38 

36 

35 

60 

61 

5° 

49 

48 

47 

46 

45 

44 

43 

42 

39 

38 

36 

61 

62 

52 

51 

50 

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48 

47 

45 

43 

42 

41 

41 

39 

38 

62 

63 

53 

52 

5° 

49 

48 

47 

45 

44 

43 

42 

39 

63 

64 

54 

53 

52 

50 

49 

48 

47 

46 

45 

43 

42 

4i 

64 

65 
66 

55 
56 

54 

55 

53 
54 

52 
53 

51 

52 

50 

49 
50 

48 
49 

s 

46 
47 

45 
46 

43 
45 

42 

44 

65 
66 

67 

57 

56 

55 

55 

54 

53 

52 

51 

5° 

48 

47 

46 

45 

67 

68 

58 

57 

57 

56 

55 

54 

53 

52 

50 

49 

47 

46 

68 

69 

59 

58 

58 

57 

56 

55 

54 

53 

52 

5° 

49 

48 

69 

70 

61 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

5° 

49 

70 

71 

62 

61 

60 

59 

58 

57 

56 

55 

55 

54 

53 

52 

71 

72 
73 

63 
64 

62 
63 

61 

62 

60 
62 

59 
61 

8 

58 
59 

56 

57 

55 
56 

54 

55 

53 

54 

52 
53 

72 
73 

74 

65 

64 

63 

63 

62 

61 

60 

59 

58 

57 

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74 

75 
76 

66 
67 

65 
66 

64 
65 

64 
65 

63 
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62 
63 

61 
62 

60 
61 

59 
61 

c 

57 

56 
58 

56 

57 

75 
76 

77 

68 

67 

67 

66 

65 

64 

63 

62 

62 

61 

60 

59 

58 

77 

78 

69 

68 

68 

67 

66 

66 

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63 

62 

61 

60 

59 

78 

79 

70 

69 

69 

68 

67 

67 

67 

65 

64 

63 

62 

61 

61 

79 

80 

72 

71 

7° 

69 

68 

68 

67 

66 

65 

64 

63 

62 

62 

80 

t 

6.0° 

6.5° 

7.0° 

7.5° 

8.0° 

8.5° 

9.0° 

9.5° 

10.0° 

10.5° 

11.0° 

11.5° 

12.0° 

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i6o 


PHYSICAL   LABORATORY   GUIDE 


X.    TEMPERATURE   OF  THE  DEW  POINT,  IN  DEGREES 
FAHRENHEIT.—  Continued 


ft 

M 

> 

(2 

DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (t-f) 

J 
1 

12.0° 

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14.0° 

14.5° 

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16.0° 

16.5° 

17.0° 

17.5° 

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40 

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40 

41 

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42 

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48 

49 

17 

14 

12 

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49 

50 

19 

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9 

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50 

51 

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18 

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-52 

51 

52 

23 

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30 

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57 

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32 

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29 

27 

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22 

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58 

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33 

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59 

60 

35 

33 

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60 

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61 

62 

38 

37 

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29 

28 

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62 

63 

39 

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29 

28 

26 

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63 

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41 

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35 

34 

32 

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22 

64 

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40 

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32 

31 

29 

28 

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65 

66 

44 

43 

41 

40 

38 

37 

35 

34 

32 

31 

30 

28 

26 

66 

67 

68 

45 
46 

44 
45 

43 
44 

43 

40 
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39 
40 

37 
39 

36 
38 

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32 

34 

31 
33 

30 

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28 

3° 

67 

68 

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48 

47 

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45 

43 

42 

40 

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38 

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34 

33 

32 

69 

70 
71 

49 

48 
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39 
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36 
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52 

51 

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44 

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40 

38 

37 

72 

73 

53 

52 

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48 

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44 

43 

41 

40 

38 

73 

74 

54 

53 

52 

5° 

49 

48 

47 

45 

44 

43 

40 

74 

75 

56 

55 

54 

53 

52 

So 

49 

48 

47 

45 

44 

43 

42 

75 

76 

57 

56 

55 

54 

53 

52 

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49 

48 

47 

46 

45 

43 

76 

77 

58 

57 

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53 

52 

51 

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49 

48 

46 

45 

77 

78 

59 

58 

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56 

55 

53 

52 

51 

50 

49 

48 

78 

79 

61 

60 

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57 

56 

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53 

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49 

48 

79 

80 

62 

61 

60 

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55 

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53 

52 

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80 

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12.0° 

12.5° 

13.0° 

13.5° 

140° 

14.5° 

15.0° 

15.5° 

16.0° 

16.5° 

17.0° 

17.5° 

18.0° 

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TABLES    OF   PHYSICAL   CONSTANTS 


161 


X.     TEMPERATURE   OF  THE  DEW  POINT,   IN  DEGREES 
FAHRENHEIT.  —  Continued 


ft 

m 

«& 
> 

K 
P 

DlFEERENCE   BETWEEN  THE   DRY   AND    WET   THERMOMETERS    (t-t') 

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1 

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19.0° 

20.0° 

21.0° 

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23.0° 

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300° 

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73 

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73 

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75 

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76 

77 

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42 

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33 

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77 

78 

47 

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38 

35 

32 

28 

24 

20 

14 

7 

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78 

79 

48 

46 

43 

40 

37 

34 

31 

27 

23 

18 

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79 

80 

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47 

45 

42 

39 

36 

32 

29 

25 

21 

15 

8 

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80 

t 

18.0° 

19.0° 

20.0° 

21.0° 

22.0° 

230° 

240° 

25.0° 

26.0° 

27.0° 

28.0° 

29.0° 

30.0° 

t 

1 62 


PHYSICAL   LABORATORY   GUIDE 


XI.    RELATIVE  HUMIDITY,   PER   CENT 


i 

^& 

DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (/-/') 

8 

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1 

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1.0° 

1.5° 

2.0° 

2.5° 

3.0° 

3.5° 

4.0° 

4.5° 

5.0° 

5.5° 

6.0° 

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M 

Q 

20 

92 

85 

77 

70 

63 

56 

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4i 

34 

27 

20 

13 

20 

21 

93 

85 

78 

71 

64 

57 

50 

43 

36 

29 

23 

16 

21 

22 

93 

86 

79 

72 

65 

58 

51 

45 

38 

32 

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19 

22 

23 

93 

86 

80 

73 

66 

60 

53 

46 

40 

34 

27 

21 

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24 

93 

87 

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74 

67 

61 

54 

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94 

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38 

32 

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25 

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94 

88 

81 

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69 

63 

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28 

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82 

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47 

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52 

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80 
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72 

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33 

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95 

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86 

82 

76 

73 

69 

65 

59 

54 

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45 

35 

36 

96 

9i 

86 

82 

77 

73 

70 

66 

61 

56 

51 

47 

36 

37 

96 

9i 

87 

82 

78 

74 

7° 

66 

62 

57 

52 

48 

37 

38 

96 

92 

87 

83 

79 

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7i 

67 

63 

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38 

39 

96 

92 

88 

83 

79 

75 

72 

68 

63 

59 

55 

52 

39 

40 

96 

92 

88 

84 

80 

76 

72 

68 

64 

60 

56 

53 

40 

41 

96 

92 

88 

84 

80 

76 

72 

69 

65 

61 

57 

54 

41 

42 
43 

96 
96 

92 
92 

88 
88 

84 
85 

81 
81 

77 
77 

73 
74 

69 

70 

s 

62 
63 

58 
59 

55 
56 

42 
43 

44 

96 

92 

88 

85 

81 

78 

74 

70 

67 

63 

60 

57 

44 

45 

96 

92 

89 

85 

82 

78 

75 

71 

67 

64 

61 

58 

45 

46 

47 

96 
96 

93 
93 

89 
89 

85 
86 

82 
83 

79 
79 

9 

72 
72 

68 
69 

Si 

61 
62 

58 
59 

46 
47 

48 

96 

93 

89 

86 

83 

79 

76 

73 

69 

66 

63 

60 

48 

49 

97 

93 

80 

86 

83 

80 

76 

73 

70 

67 

63 

60 

49 

50 

97 

93 

90 

87 

83 

80 

77 

74 

70 

67 

64 

61 

50 

51 

97 

93 

90 

87 

84 

81 

77 

74 

71 

68 

65 

62 

51 

52 

97 

94 

90 

87 

84 

81 

78 

75 

72 

69 

66 

63 

52 

53 

97 

94 

9i 

87 

84 

81 

78 

75 

72 

69 

66 

63 

53 

54 

97 

94 

9i 

88 

85 

82 

79 

76 

73 

7° 

67 

64 

54 

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0.5° 

1.0° 

1.5° 

20° 

2.5° 

3.0° 

3.5° 

40° 

4.5° 

5.0° 

5.5° 

60° 

t 

TABLES   OF   PHYSICAL   CONSTANTS  163 

XI.    RELATIVE  HUMIDITY,  PER   CENT.— Continued 


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DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (t  -  1')  • 

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55 

97 

94 

91 

88 

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76 

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90 

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0.5° 

1.0° 

1.5° 

2.0° 

2.5° 

3.0° 

3.5° 

4.0° 

4.5° 

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1 64  PHYSICAL   LABORATORY    GUIDE 

XI.     RELATIVE   HUMIDITY,   PER   CENT.—  Continued 


I 

M 

P 

.  DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (t—t'} 

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6.0° 

6.5° 

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8.5° 

9.0° 

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11.0° 

11.5° 

12.0° 

19 

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19 

20 

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20 

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16 

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23 

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24 

25 

26 

2O 

J4 

8 

3 

25 

26 

28 

23 

17 

ii 

6 

26 

27 

3° 

25 

19 

14 

9 

3 

27 

28 

33 

27 

22 

17 

ii 

6 

I 

28 

29 

35 

29 

24 

19 

H 

9 

4 

29 

30 

36 

31 

26 

22 

12 

7 

2 

30 

31 

38 

33 

29 

24 

19 

14 

10 

5 

31 

32 

40 

35 

31 

26 

21 

17 

12 

8 

3 

32 

33 

42 

37 

33 

28 

24 

19 

J5 

10 

6 

2 

33 

34 

44 

•39 

35 

30 

26 

21 

17 

13 

9 

4 

34 

35 

45 

37 

32 

28 

24 

19 

15 

12 

7 

3 

35 

36 

47 

43 

38 

34 

3° 

26 

22 

18 

14 

10 

6 

2 

36 

37 

48 

44 

40 

36 

32 

28 

24 

20 

16 

12 

8 

5 

I 

37 

38 

5° 

46 

42 

38 

34 

30 

26 

22 

18 

15 

ii 

7 

3 

38 

39 

52 

48 

44 

40 

36 

32 

28 

24 

20 

17 

13 

9 

6 

39 

40 

53 

49 

45 

38 

34 

30 

26 

22 

19 

16 

12 

8 

40 

41 

54 

5° 

46 

43 

39 

36 

32 

29 

24 

21 

18 

*4 

10 

41 

42 

55 

51 

48 

44 

40 

37 

34 

30 

27 

23 

20 

16 

'3 

42 

43 

56 

S2 

49 

46 

42 

38 

35 

32 

29 

25 

22 

19 

15 

43 

44 

57 

53 

5° 

47 

43 

40 

37 

33 

30 

27 

24 

21 

17 

44 

45 

58 

54 

48 

44 

38 

32 

29 

25 

22 

19 

45 

46 

58 

55 

52 

49 

46 

42 

39 

36 

33 

30 

27 

23 

21 

46 

47 

59 

56 

53 

5° 

47 

44 

40 

38 

34 

31 

28 

25 

22 

47 

48 

60 

56 

53 

51 

48 

45 

42 

39 

36 

33 

3° 

27 

24 

48 

49 

60 

57 

54 

52 

49 

46 

43 

40 

37 

34 

31 

29 

26 

49 

t 

6.0° 

6.5° 

7.0° 

7.5° 

8.0° 

8.5° 

9.0° 

9.5° 

10.0° 

'10.5° 

11.0° 

11.5° 

12.0° 

t 

TABLES    OF    PHYSICAL  CONSTANTS  165 

XI.   RELATIVE   HUMIDITY,   PER   CENT.— Continued 


D 

*S 

Q 

DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (/-/') 

| 

~£ 

>H 

M 

q 

6.0° 

6.5° 

7.0° 

7.5° 

8.0° 

8.5° 

9.0° 

9.5° 

10.0° 

10.5° 

11.0° 

11.5° 

12.0° 

50 

61 

58 

55 

52 

5° 

47 

44 

41 

38 

36 

33 

3° 

27 

50 

51 

62 

59 

56 

53 

5° 

48 

45 

42 

39 

37 

34 

3i 

28 

51 

52 

63 

60 

57 

54 

5i 

48 

46 

43 

40 

38 

35 

33 

30 

52 

53 

63 

6l 

58 

55 

52 

49 

47 

44 

42 

39 

36 

34 

31 

53 

54 

64 

61 

59 

56 

53 

50 

48 

45 

43 

40 

38 

35 

32 

54 

55 

65 

62 

59 

57 

54 

51 

49 

46 

43 

4i 

39 

36 

34 

55 

56 

65 

63 

60 

57 

55 

52 

5° 

47 

44 

42 

40 

37 

35 

56 

57 

66 

64 

61 

58 

55 

53 

5° 

48 

45 

43 

40 

38 

36 

57 

58 

67 

64 

61 

59 

56 

53 

51 

49 

46 

44 

42 

39 

37 

58 

59 

67 

65 

62 

60 

57 

54 

52 

49 

47 

45 

43 

40 

38 

59 

60 

69 

65 

63 

60 

58 

55 

53 

5° 

48 

46 

44 

4i 

39 

60 

61 

68 

66 

63 

61 

58 

56 

54 

51 

49 

47 

44 

42 

40 

61 

62 

69 

66 

64 

61 

59 

57 

54 

52 

5° 

47 

45 

43 

4i 

62 

63 

69 

67 

64 

62 

60 

57 

55 

53 

51 

48 

46 

44 

42 

63 

64 

70 

67 

65 

62 

60 

58 

56 

53 

5i 

49 

47 

45 

43 

64 

65 

70 

68 

65 

63 

61 

59 

56 

54 

S2 

50 

48 

46 

44 

65 

66 

71 

68 

66 

63 

61 

59 

57 

55 

53 

51 

49 

47 

45 

66 

67 

7i 

69 

66 

64 

62 

60 

58 

55 

53 

51 

49 

47 

45 

67 

68 

7i 

69 

67 

65 

63 

60 

58 

56 

54 

52 

50 

48 

46 

68 

69 

72 

7° 

67 

65 

63 

61 

59 

57 

55 

53 

51 

49 

47 

69 

70 

72 

70 

68 

66 

64 

62 

60 

57 

55 

53 

52 

5° 

48 

70 

71 

72 

70 

68 

66 

64 

62 

60 

58 

56 

54 

52 

50 

48 

71 

72 

73 

71 

69 

67 

65 

63 

61 

59 

57 

55 

53 

51 

49 

72 

73 

73 

7i 

69 

67 

65 

63 

61 

59 

57 

55 

53 

52 

5° 

73 

74 

74 

72 

70 

68 

66 

64 

62 

60 

58 

56 

54 

52 

50 

74 

75 

74 

72 

70 

68 

66 

64 

62 

60 

58 

56 

55 

53 

5i 

75 

76 

74 

72 

70 

68 

66 

64 

63 

61 

59 

57 

55 

53 

52 

76 

77 

74 

73 

71 

69 

67 

65 

63 

61 

59 

57 

56 

54 

52 

77 

78 

75 

73 

71 

69 

67 

65 

63 

62 

60 

58 

56 

54 

53 

78 

79 

75 

73 

7i 

70 

68 

66 

64 

62 

60 

58 

57 

55 

53 

79 

80 

75 

73 

72 

7° 

68 

66 

64 

63 

61 

59 

57 

55 

54 

80 

t 

6.0° 

65° 

7.0° 

7.5° 

8.0° 

8.5° 

9.0° 

9.5° 

10.0° 

10.5° 

11.0° 

11.5° 

12.0° 

t 

1 66 


PHYSICAL   LABORATORY   GUIDE 


XI.   RELATIVE  HUMIDITY,  PER  CENT.  —  Continued 


pi 

jjj 

DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (t—  t') 

jjj 

1 

120° 

12.5° 

13.0° 

13.5° 

14.0° 

14.5° 

15.0° 

15.5° 

16.0° 

16.5° 

17.0° 

17.5° 

18.0" 

Q 

40 

8 

5 

i 

40 

4i 

10 

7 

4 

41 

4. 

13 

10 

6 

3 

42 

4  > 

IS 

12 

9 

5 

2 

43 

44 

17 

14 

ii 

8 

5 

i 

44 

45 

Ig 

16 

13 

10 

7 

4 

i 

45 

46 

21 

18 

15 

12 

9 

6 

3 

46 

47 

22 

20 

16 

M 

ii 

8 

5 

3 

47 

48 

24 

21 

19 

16 

13 

10 

7 

5 

2 

48 

49 

26 

23 

20 

17 

IS 

12 

9 

7 

4 

i 

49 

50 

27 

24 

22 

19 

16 

H 

n 

9 

6 

4 

i 

50 

51 

28 

26 

23 

21 

18 

16 

13 

10 

8 

5 

3 

51 

52 
53 

3° 
31 

27 
29 

Ii 

22 

24 

20 
21 

17 
19 

11 

12 
14 

10 
12 

7 
9 

5 
7 

4 

2 

52 
53 

54 

32 

30 

28 

25 

23 

20 

18 

15 

13 

ii 

8 

6 

4 

54 

55 

34 

31 

29 

26 

24 

22 

19 

17 

15 

12 

10 

8 

6 

55 

56 

35 

33 

30 

28 

25 

23 

21 

19 

16 

14 

12 

10 

8 

56 

57 

36 

34 

29 

27 

24 

22 

20 

18 

16 

13 

ii 

9 

57 

58 

37 

35 

33 

30 

28 

26 

24 

21 

19 

«7 

15 

13 

ii 

58 

59 

38 

36 

34 

31 

29 

27 

25 

23 

21 

18 

16 

12 

59 

60 

39 

37 

34 

32 

30 

28 

26 

24 

22 

20 

18 

16 

M 

60 

61 
62 

40 

38 
39 

35 
37 

33 
34 

32 
32 

29 
30 

3 

3 

23 

21 
22 

20 

18 

15 
16 

61 
62 

63 
64 

42 
43 

40 

i 

H 

33 
34 

31 
32 

29 
30 

28 

29 

27 

24 
25 

22 

23 

20 

21 

18 
19 

63 
64 

65 

44 

42 

39 

37 

35 

33 

3' 

29 

28 

26 

24 

22 

20 

65 

66 
67 

68 

45 
45 
46 

42 
43 
44 

40 
42 

38 
39 
40 

36 
37 
38 

34 

H 

32 
33 
34 

30 
32 
33 

29 
30 

2 

29 

11 

27 

23 
25 

26 

22 
23 
24 

66 
67 
68 

69 

47 

45 

43 

39 

37 

35 

33 

32 

3° 

28 

26 

25 

69 

70 

48 

46 

44 

42 

40 

38 

36 

34 

33 

3i 

29 

27 

26 

70 

71 

48 

46 

45 

43 

41 

39 

37 

35 

34 

32 

30 

28 

27 

71 

72 

49 

47 

45 

43 

42 

40 

38 

36 

35 

33 

31 

3° 

28 

72 

73 
74 

5° 
5° 

48 
48 

46 
47 

44 
45 

42 
43 

41 

39 
40 

Ii 

9 

34 
35 

32 
33 

30 
31 

29 

3° 

73 
74 

75 

51 

49 

47 

46 

44 

42 

40 

39 

37 

35 

34 

32 

31 

75 

76 

52 

50 

48 

46 

45 

43 

41 

39 

38 

36 

35 

33 

31 

76 

77 

52 

5° 

49 

47 

45 

44 

42 

40 

39 

37 

35 

34 

32 

77 

78 

53 

49 

48 

46 

44 

43 

39 

38 

36 

35 

33 

78 

79 

53 

52 

50 

48 

47 

45 

43 

42 

40 

39 

37 

36 

34 

79 

80 

54 

52 

51 

49 

47 

45 

44 

42 

4i 

39 

38 

36 

35 

80 

t 

12.0° 

12.5° 

13.0° 

13.5° 

14.0° 

14.5° 

15.0° 

15.5° 

16.0° 

16.5° 

17.0° 

175= 

18.0° 

t 

TABLES    OF   PHYSICAL   CONSTANTS 


167 


XL   RELATIVE  HUMIDITY,   PER   CENT.  — Continued 


'j. 
M 

J 

5 

g 

DIFFERENCE  BETWEEN  THE  DRY  AND  WET  THERMOMETERS  (/-*') 

§ 
Q 

18.0° 

19.0° 

20.0° 

21.0° 

22.0° 

23.0° 

24.0° 

25.0° 

26.D 

27.0° 

28.0° 

29.0^ 

30.0 

re 

6 

j 

55 

56 

8 

3 

56 

57 

9 

5 

57 

53 

ii 

7 

2 

58 

59 

12 

8 

4 

59 

60 

14 

10 

6 

2 

60 

61 

15 

ii 

7 

3 

61 

62 

16 

13 

9 

5 

62 

63 

18 

H 

10 

7 

3 

63 

64 

19 

15 

12 

8 

5 

I 

64 

65 

20 

17 

13 

10 

6 

3 

65 

66 

22 

18 

14 

ii 

8 

4 

i 

66 

67 

23 

19 

16 

12 

9 

6 

2 

67 

68 

24 

20 

J7 

14 

10 

7 

4 

i 

68 

69 

25 

22 

18 

15 

12 

8 

5 

2 

69 

70 

26 

23 

19 

16 

13 

10 

7 

4 

I 

70 

71 

27 

24 

20 

17 

14 

ii 

8 

5 

2 

71 

72 

28 

24 

22 

18 

15 

12 

9 

6 

3 

I 

72 

73 

29 

22 

19 

16 

13 

10 

8 

2 

73 

74 

30 

26 

23 

20 

18 

15 

12 

9 

6 

3 

I 

74 

75 

31 

27 

24 

21 

19 

16 

13 

10 

7 

5 

2 

75 

76 

31 

28 

25 

22 

20 

17 

14 

ii 

8 

6 

3 

I 

76 

77 

32 

29 

26 

23 

20 

18 

15 

12 

10 

7 

4 

2 

77 

78 
79 

33 
34 

30 

31 

3 

24 

25 

21 

22 

19 
19 

17 

13 
14 

ii 

12 

9 

6 

7 

3 
4 

I 

2 

•78 
79 

80 

35 

32 

29 

26 

23 

20 

18 

15 

13 

10 

8 

6 

3 

80 

t 

18.0° 

19.0° 

20.0° 

21.0° 

22.0° 

23.0° 

24.0° 

25.0° 

26.0° 

27.0° 

28.0°29.0 

30.0° 

t 

1                  Ii 

1 

FHYS.  LAB.  GUIDE  —  12 


1 68 


PHYSICAL   LABORATORY   GUIDE 


XII.     INDICES   OF  REFRACTION 


Air                           .     . 

I  000294 

Ice  

.31 

Alcohol    

1.36 

Iceland  spar,  ordinary  ray    . 

.65 

Canada  balsam  .     .     . 

1.54 

i  68 

Iceland   spar,  extraordinary 
rav 

.48 

2  A  7  to  2  7^ 

\Vater  

.336 

Ether  

1.36 

The  eye  : 

Glass,  crown     .     .     . 
Glass,  flint    .... 
Glycerine      .... 

1.53  to  1.56 
1.58  to  1.64 

1.47 

Aqueous  humor    .     . 
Vitreous  humor 
Crystalline  lens     .     . 

•337 
•339 
•3^4 

XIII.     SPECIFIC   HEATS 


Acetic  acid 0.6589 

Acetone °-53° 

Alcohol,  ethyl  (o°-5O°)  .     .0.615 

Air 0.2374 

Alcohol,  methyl  (o°-6i°)    .  0.613 
Aluminum  (i5°-97°)  .     .     •  0.2122 
Antimony  (o°-ioo°)    .     .     .  0.0507 

Beeswax 0.64 

Benzene  (n°-8i°)      .     .     .  0.45 
Bismuth  (9°-iO2°)      .     .     .  0.0298 
Brass,  hard  (o°-ioo°)      .     .  0.0858 
Carbon  disulphide  (34°-6o°)  0.2206 
Copper  (o°-ioo°)  ....  0.0949 

Ether  (o°-33°) 0.517 

Glass,  thermometer (o°-ioo°)  0.1770 
Glycerine  (o°-ioo°)    .     .     .  0.555 
Hydrogen 3.409 


Ice 

Iron  (o°-ioo°)  .     , 

Lead  (i9°-48°)       . 
Marble  .     .     . 

Mercury  (o°-ioo°) 
Nickel  (i4°-97°) 


0.504 

0.1098 

0.0315 

0.2129 

0-0333 

0.1217 


Nitrogen 0.2438 

Olive  oil 0.310 

Oxygen 0.2175 

Platinum  (o°-ioo°)     .     .     .  0.0355 

Silver  (o°-ioo°)      ....  0.0559 

Salt 0.173 

Sulphur  (i5°-95°).     .     .     -  0.1844 

Steel 0.118 

Tin  (o°-ioo°) 0.0559 

Turpentine  (o°-ioo°).     .     .  0.426 

Zinc  (o°-ioo°) °-°935 


XIV.     SPECIFIC  RESISTANCES 


RESISTANCE  IN  OHMS 

RESISTANCE  IN  OHMS 

TEMPERATURE  COEF- 

OF WIRE  100  CM. 

OF  WIRE  i  FOOT 

FICIENT  (INCREASE 

LONG  AND  i  MM. 

LONG  AND  i  MIL. 

OF  RESISTANCE)  OF 

IN  DIAMETER  AT 

DIAMETER  AT 

i  OHM  FOR  A  RISE  IN 

TEMPERATURE  o°  C. 

TEMPERATURE  o°  C. 

TEMPERATURE  i°  C. 

Aluminum 

0.03699 

17.48 

0.00388 

Copper      .     .     . 

O.O2O62 

10.19 

0  00388 

German  silver    . 

0.2660 

181.3 

0.00044 

Iron      .... 

0.1234 

61.3 

0.00055 

Mercury    . 

1.198 

574-0 

0.00072 

Platinum  .     .     . 

o.i  150 

7°-5 

Silver   .... 

0.02019 

9-53 

0.00377 

TABLES   OF   PHYSICAL   CONSTANTS  169 

XV.     TABLE  OF  NATURAL   SINES  AND   TANGENTS 


ANGLE 

SINE 

TANGENT 

ANGLE 

SINE 

TANGENT 

ANGLE 

SINE 

TANGENT 

Degrees 

Degrees 

Degrees 

0 

o.ooo 

O.OOO 

31 

°-SlS 

0.601 

62 

0.883 

I.88I 

1 

0.017 

0.017 

32 

0.530 

0.625 

63 

0.891 

1.963 

2 

0.035 

0-035 

33 

0-545 

0.649 

64 

0.899 

2.050 

3 

0.052 

0.052 

34 

o-559 

0.675 

65 

0.906 

2.145 

4 

0.070 

0.070 

35 

o-574 

0.700 

66 

0.914 

2.246 

5 

0.087 

0.087 

36 

0.588 

0.727 

67 

0.921 

2.356 

6 

0.105 

0.105 

37 

0.602 

o-754 

68 

0.927 

2-475 

7 

0.122 

0.123 

38 

0.616 

0.781 

69 

0-934 

2.605 

8 

0.139 

0.141 

39 

0.629 

0.810 

70 

0.940 

2.747 

9 

0.156 

0.158 

40 

0.643 

0.839 

71 

0.946 

2.904 

10 

0.174 

0.176 

41 

0.656 

0.869 

72 

0.951 

3.078 

11 

O.I9I 

0.194 

42 

0.669 

0.900 

73 

0.956 

3-271 

12 

0.208 

0.213 

43 

0.682 

0-993 

74 

0.961 

3487 

13 

0.225 

0.231 

44 

0.695 

0.966 

75 

0.966 

3-732 

14 

0.242 

0.249 

45 

0.707 

I.OOO 

76 

0.970 

4.011 

15 

0.259 

0.268 

46 

0.719 

1.036 

77 

0.974 

4-331 

16 

0.276 

0.287 

47 

0-731 

1.072 

78 

0.978 

4-7°5 

17 

0.292 

0.306 

48 

o-743 

I.  Ill 

79 

0.982 

5-H5 

18 

0.309 

0-325 

49 

0-755 

1.150 

80 

0.985 

5.671 

19 

0.326 

0-344 

50 

0.706 

1.192 

81 

0.988 

6.314 

20 

0.342 

0.364 

51 

0.777 

L235 

82 

0.990 

7-U5 

21 

0.358 

0.384 

52 

0.788 

1.280 

83 

0-993 

8.144 

22 

°-375 

0.404 

53 

0-799 

1-327 

84 

0-995 

9-5l4 

23 

0.391 

0.424 

54 

0.809 

I.376 

85 

0.996 

n-43 

24 

0.407 

0-445 

55 

0.819 

1.428 

86 

0.998 

14.30 

25 

0.423 

0.466 

56 

0.829 

1.483 

87 

0.999 

19.08 

26 

0.438 

0.488 

57 

0.839 

1.540 

88 

0.999 

28.64 

27 

0.454 

0.510 

58 

0.848 

i.  600 

89 

I.OOO 

57-29 

28 

0.469 

0.532 

59 

0.857 

1.664 

90 

I.OOO 

OO 

29 

0.485 

o-554 

60 

0.866 

I-732 

30 

0.500 

0-577 

61 

0.875 

1.804 

PHYSICAL   LABORATORY   GUIDE 


XVI.    NUMBER,  DIAMETER,  WEIGHT,  LENGTH,  AND 
RESISTANCE  OF  PURE   COPPER  WIRE 

BROWN  AND  SHARPE  GAUGE 


No. 

* 

DlAM. 

IN  MILS 

CIRCULAR 
MILS  (DR.) 

I    MlL  = 

.001  IN. 

WEIGHT, 
POUNDS 

PER 
IOOO   FT. 

LENGTH, 
FEET  PER 
POUND 

RESISTANCE  OF  PURE  COPPER  AT 
75°  F. 

Ohms  per 

IOOO  ft. 

Feet  per 
Ohm 

Ohms  per 
Pound 

oooo 

460.000 

211600.0 

639.32 

1.56 

0.051 

19605.69 

0.0000798 

000 

409.640 

167805.0 

507.01 

1.97 

0.064 

15547.87 

0.000127 

00 

364.800 

I33079.2 

402.09 

2.49 

0.081 

12330.36 

0.000202 

0 

324-95° 

105534.0 

319.04 

3-!3 

0.102 

9783.63 

0.000320 

I 

289.300 

83694.0 

252.88 

3.95 

0.129 

7754.66 

0.00051 

2 

257.630 

66373.0 

200.04 

4.99 

0.163 

6149.78 

O.OOOSII 

3 

229.420 

526334 

159-03 

6.29 

0.205 

4876.73 

0.001289 

4 

204.310 

41742.5 

126.12 

7-93 

0.259 

3867.62 

0.00205 

5 

181.940 

33I02-3 

IOO.OI 

10.00 

0.326 

3067.06 

0.00326 

6 

162.020 

26250.5 

79-32 

12.61 

0.411 

2432.22 

0.00518 

7 

144.280 

20817.0 

62.90 

15.90 

0.519 

1928.75 

0.00824 

8 

128.490 

16509.0 

49.88 

20.05 

0.654 

1529.69 

O.OI3II 

9 

114.430 

13094.0 

39-56 

25.28 

0.824 

1213.22 

0.02083 

10 

101.890 

10381.0 

3J-37 

31.88 

1.040 

961.91 

0.03314 

it 

90.742 

8234.1 

24.88 

40.20 

1.311 

762.93 

0.05269 

12 

80.808 

6529.9 

19-73 

50.69 

1.653 

605.03 

0.08377 

13 

71.961 

5I78-4 

I5-65 

63.91 

2.084 

479.80 

O.I332I 

*4 

64.084 

4106.8 

12.41 

80.59 

2.628 

380.51 

0.2II8 

15 

57.068 

3256.8 

9.84 

101.63 

3.314 

301.75 

0.3368 

16 

50.820 

2582.7 

7.81 

128.14 

4.179 

239.32 

0-5355 

17 

45-257 

2048.2 

6.19 

161.59 

5.269 

189.78 

0.8515 

18 

40-303 

1624.3 

4.91 

203.76 

6.645 

150-50 

1.3539 

19 

35.890 

1288.1 

3.78 

264.26 

8.617 

116.05 

2.2772 

20 

31.961 

1021.5 

3.09 

324.00 

10.566 

94.65 

3423 

21 

28.462 

810.08 

2-45 

408.56 

13.323 

75.06 

5-443 

22 
23 

25-347 
22.571 

642.47 
509-45 

1.94 
1-54 

SIS-IS 
649.66 

16.799 
21.185 

59-53 
47.20 

8.654 
13-763 

24 

2O.IOO 

504.01 

1.22 

819.21 

26.713 

3743 

21.885 

17.900 

320.41 

0.97 

1032.96 

33.684 

29.69 

34-795 

26 

15.940 

254.08 

0.77 

1302.61 

42.477 

23-54 

55-331 

27 

I4-I95 

201.50 

0.6  1 

1642.55 

53.563 

18.68 

87.979 

28 

12.641 

159-79 

0.48 

2071.22 

67.542 

14.81 

139.893 

29 

11.257 

126.72 

0.38 

2611.82 

85.170 

11.74 

222.449 

3° 

10.025 

100.50 

0.30 

3293.97 

107.391 

9.31 

353-742 

31 

8.928 

79.71 

0.24 

4152.22 

135.402 

7.39 

562.221 

S2 

7.950 

63.20 

0.19 

5236.66 

170.765 

5.86 

894.242 

33 

7.080 

5°-*3 

0.15 

6602.71 

215.312 

4-64 

1421.646 

34 

6.304 

39-74 

O.I2 

8328.30 

27I-583 

3-68 

2261.82 

5.614 

3J-52 

O.IO 

10501.35 

342.443 

2.92 

3596.104 

36 

5.000 

25.00 

0.08 

13238.83 

431.712 

2.32 

57I5.36 

37 

4-453 

19.83 

O.O6 

16691.06 

544.287 

1.84 

9084.71 

38 

3-965 

15.72 

O.O5 

20854.65 

686.511 

1.46 

14320.26 

39 

3-531 

12.47 

0.04 

26302.23 

865.046 

1.16 

2^752.6 

40 

3-J44 

9.88 

0.03 

33*75-94 

1091.865 

0.92 

36223.59 

TABLES    OF   PHYSICAL   CONSTANTS 


XVII.  ELECTRICAL  RESISTANCE,  DIAMETER,  CROSS  SEC- 
TION, ETC.,  OF  COPPER  WIRE,  AMERICAN  GAUGE, 
TEMPERATURE  24°  C. 


d 
% 

J 

SIZE 

WEIGHT 

RESISTANCE 

CAPACITY 

IN 

AMPERES 

Diam. 
Inches 

Area 
Sq.  In. 

Lb.  per 
1000  Ft. 

Feet  per 
Pound 

Ohms  per 
looo  Ft. 

Feet  per 
Ohm 

Ohms  per 
Pound 

0000 

.4600 

.166191 

639.60 

1.564 

0.051 

19929.7 

0.0000785 

312.0 

000 

.4096 

.131790 

507.22 

1.971 

0.063 

15804.9 

0.000125 

262.0 

00 

.3648 

.104590 

402.25 

2.486 

0.080 

12534.2 

0.000198 

22O.O 

0 

.3249 

.082932 

319.17 

3-133 

O.IOI 

9945-3 

0.000315 

185.0 

1 

.2893 

•065733 

252.93 

3.952 

0.127 

7882.8 

0.000501 

156.0 

2 

.2576 

.052130 

200.63 

4-994 

0.160 

6251.4 

0.000799 

I3I.O 

3 

.2294 

.041339 

159.09 

6.285 

0.202 

4957-3 

0.001268 

IIO.O 

4 

.2043 

.032784 

126.17 

7.925 

0.254 

3931-6 

0.002016 

92.3 

5 

.1819 

.025998 

100.05 

9-995 

0.321 

3117.8 

0.003206 

77-6 

6 

.1620 

.020617 

79-34 

12.604 

0.404 

2472.4 

0.005098 

65-2 

7 

•1443 

.016349 

62.92 

I5.893 

0.509 

1960.6 

0.008106 

54-8 

8 

.1285 

.012766 

49.90 

20.040 

0.643 

JSSS-o 

0.01289 

46.1 

9 

.1144 

.010284 

39.58 

25-265 

0.811 

1233-3 

0.02048 

38.7 

10 

.1014 

.008153 

31-38 

31.867 

1.023 

977.8 

0.03259 

32.5 

11 

.0907 

.•006467 

24.89 

40.176 

1.289 

775-5 

0.05181 

27-3 

12 

.0808 

.005129 

19.74 

50.651 

1.126 

615.02 

0.08237 

23.0 

13 

.0720 

.004067 

*S'(>5 

63.898 

2.048 

488.25 

0.13087 

19.2 

14 

.0641 

.003147 

12.41 

80.580 

2.585 

386.80 

0.20830 

16.2 

15 

.0571 

.002558 

9.84 

101.626 

3-!77 

306.74 

o.33x33 

13.6 

16 

.0508 

.002029 

7.8! 

128.041 

4.582 

243-25 

0.52638 

"•5 

17 

•0453 

.001609 

6.19 

161.551 

5-183 

192.91 

0.83744 

9-6 

18 

.0403 

.001276 

4.91 

203.666 

6.536 

152.99 

i-3312 

8.1 

19 

•0354 

.000984 

3.786 

264.136 

8.477 

117.96 

2.2392 

6.7 

20 

.0320 

.000802 

3.086 

324.045 

10.394 

96.21 

3.3438 

57 

21 

.0285 

.000636 

2.448 

408.497 

13.106 

76.30 

5-3539 

4.8 

22 

•0253 

.000505 

1.942 

5I4.933 

16.525 

60.51 

8.5099 

4.0 

23 

.0226 

.000400 

J-539 

649773 

20.842 

47.98 

13-334 

3-4 

24 

.O2OI 

.000317 

I.22I 

819.001 

26.284 

38.05 

21.524 

2.8 

25 

.0179 

.000252 

0.967 

1034.126 

33-135 

30.18 

34-298 

2-4 

26 

.0159 

.000199 

0.768 

1302.083 

41.789 

23.93 

54410 

2.0 

27 

.0142 

.000158 

0.608 

1644.737 

52.687 

18.98 

86.657 

1-7 

28 

.0126 

.000125 

0.484 

2066.116 

66.445 

15-05 

137.283 

1.4 

29 

.0113 

.OOOIOO 

0.384 

2604.167 

83752 

11.94 

218.104 

1.2 

30 

.oioo 

.000079 

0.302 

33H-258 

105.641 

9.466 

349.805 

I.O 

31 

.0089 

.000063 

0.239 

4184.100 

133.191 

7.508 

557.286 

0.84 

32 

.0079 

.000050 

0.190 

5263.158 

168.011 

5.952 

884.267 

0.70 

33 

.0071 

.000039 

O.I5I 

6622.517 

211.820 

4.721 

1402.78 

O.6o 

34 

.0063 

.000031 

O.I2I 

8264463 

267.165 

3.743 

2207.98 

0.50 

35 
36 

.0056 
.0050 

.000025 

.000020 

0.094 
0.075 

10638.30 
13333-33 

336.81 
42465 

2.969 
2-355 

3583.12 
5661.71 

0.42 
0-35 

37 

.0045 

.000016 

0.000 

535-33 

1.868 

8922.20 

0.27 

38 

.0040 

.000012 

0.045 

22222.22 

675.22 

1481 

15000.5 

0.25 

39 

•0035 

.000010 

0.038 

26315.79 

851.789 

1.174 

22415.5 

0.21 

40 

.0031 

.000008 

0.030 

33333-33 

1074.11 

0.931 

35803.8 

O.I7 

1 72 


PHYSICAL   LABORATORY    GUIDE 


XVHI.    RESISTANCES   OF  GERMAN   SILVER  WIRE 

AMERICAN  GAUGE 


SIZE 

18% 

30% 

OHMS 

PER  1000  Fl. 

OHMS 
PER  POUND 

OHMS 

PER  1000  FT. 

OHMS 
PER  POUND 

Number 

8 

11.772 

0.23598 

17.658 

0.36397 

9 

11.832 

0-37494 

17.748 

0.56241 

10 

18.72 

0.59652 

28.08 

0.89478 

11 

23-598 

0.94842 

35-397 

1.42263 

12 

29.754 

1.50786 

44.631 

2.26179 

13 

37-512 

2.39778 

56.268 

3.59667 

14 

47.304 

3.8124 

70.956 

5.7186 

15 

59.652 

6.0624 

89.478 

9.0936 

16 

75-222 

9.639 

112.833 

14.458 

17 

94.842 

I5-327 

142.263 

22.990 

18 

119.61 

24.3702 

179.41 

36.5553 

19 

155.106 

40.9896 

232.659 

61.4844 

20 

190.188 

61.614 

285.282 

92.421 

21 

239.814 

97-974 

359-721 

146.96! 

22 

302.382 

155-772 

453-573 

233.658 

23 

38i.33 

247-734 

57^99 

371.601 

24 

480.834 

393-93 

721.251 

590.89 

25 

606.312 

626.31 

909.468 

939.46 

26 

764.586 

995-958 

1146.879 

1493-937 

27 

964.134 

1583.622 

1446.201 

2375-433 

28 

1215.756 

2518.075 

1823.634 

3777.112 

29 

1533.06 

4004.082 

2299.59 

6006.123 

30 

i933-038 

6368.356 

2899.557 

9552.354  . 

31 

2437.236 

10119.978 

3655.854 

15179.967 

32 

3073.77 

16096.356 

4610.65 

24144.534 

33 

3875.616 

25589.628 

5813.424 

38384.442 

34 

4888.494 

40712.76 

7332-741 

61069.14 

35 

6163.974 

64729.87 

9245.961 

97094.80 

36 

7770.816 

102876.482 

11656.224 

i543I4-723 

37 

9797.166 

163524.78 

14695.749 

245287.17 

38 

12357.198 

257764.68 

I8535.797 

386647.02 

39 

15570.828 

409546.8 

23356.242 

614320.2 

40 

19653.57 

652024.62 

29480.35 

978036.93 

TABLES    OF   PHYSICAL   CONSTANTS 


XIX.    VELOCITY   OF   SOUND   AT  0°  C. 


METERS 

METERS 

Air 

per  sec. 

332 

Hydrogen 

per  sec. 

1269 

Ash 

per  sec. 

4668 

Iron 

per  sec. 

5I27 

Brass 

per  sec. 

3318 

Lead 

per  sec. 

1228 

Caoutchouc 

per  sec. 

60 

Maple 

per  sec. 

4106 

Carbon  monoxide 

per  sec. 

337 

Oak 

per  sec. 

3847 

Carbon  dioxide 

per  sec. 

261 

Oxygen 

per  sec. 

317 

Cedar 

per  sec. 

5°30 

Pine 

per  sec. 

3322 

Chlorine 

per  sec. 

206 

Silver 

per  sec. 

2607 

Copper 

per  sec. 

3556 

Steel 

per  sec. 

5237 

Elm 

per  sec. 

4120 

Tallow 

per  sec. 

357 

Ether 

per  sec. 

"59 

Turpentine  at 

24°  per  sec. 

J2I2 

Fir 

per  sec. 

4638 

Walnut 

per  sec. 

4601 

Glass 

per  sec. 

5026 

Water  at  8.1° 

per  sec. 

J435 

Gold 

per  sec. 

1743 

Wax 

per  sec. 

857 

CHAPTER   XII 

(a)    APPARATUS   REQUIRED    FOR  THIS   BOOK 
(6)    SOME   USEFUL   HOME-MADE   APPARATUS 

NOTE.  —  A  great  saving  in  apparatus  required  may  be  effected :  (a)  By 
having  two  pupils  work  together. 

(£)  With  more  advanced  pupils  the  author  has  tried  the  plan  of  having 
five  different  experiments  in  one  laboratory  period  and  repeating  these  same 
experiments  for  five  successive  periods.  With  costly  apparatus  this  is  a  great 
advantage,  and  also  develops  self-reliance  in  the  pupil. 

LIST  OF  APPARATUS 

Ammeter,  1  amperes,  (22),  (33).  (34),  (35). 

Alcohol,  (12),  (13),  (14),  (15),  (16),  (43). 

Blue-print  paper  (6£"  x  8£"),  Eastman's,  (18). 

Board  (8"  x  14"),  with  slot,  (18). 

Bunsen  burner,  low  form,  (23),  (32),  and  (46-52). 

Block,  rectangular,  weighted,  (i),  (37),  (39),  (43),  (56). 

Balance  scalepan,  (4),  (7-15),  (49),  (5°)>  (50>  (52),  (22). 

Balance  spring  (0-250  gm.),  (6),  (37),  (38),  (43). 

Balance  spring  (0-30  lb.),  (0-15  kgm.),  (41),  (42). 

Bottle,  wide-mouth,  ground  stopper,  4-oz.,  (13). 

Balancing  column  tubes,  (16). 

Beeswax. 

Boyle's  law  tube,  "  J  "  form,  (45). 

Barometer,  mercury  preferred,  (45),  (46). 

Boiler,  steam,  with  attachments,  (46),  (47),  (48),  (49),  (50-52). 

Beaker  (or  wide-mouth  bottle),  8-oz.,  (46). 

Block,  small,  with  vertical,  black  mark,  (56). 

Bristles,  (63). 

Bow,  bass  viol,  (63  and  65). 

175 


176  PHYSICAL  LABORATORY   GUIDE 

Balance  holders,  large  and  small,  for  horizontal  position,  (37),  (38), 

(43),  (40,  (42). 

Bar  magnets,  2  (6"  x  i"),  (17),  (18). 
Compass  (small  pocket,  scale  in  degrees),  (17),  (19),  (20). 
Cell,  simple  voltaic  (special  form),  (21)  (see  Chap.  XII). 
Cell,  Daniell,  2,  (22),  (24-26),  (28),  (29),  (30). 
Cell,  dry,  (23),  (26),  (31),  (32). 
Coil,  copper,  temperature  coefficient,  (32). 
Catch  bucket,  (7),  (8). 
Cylinder,  wood-weighted,  floating,  (8). 
Copper  sulphate,  (12),  (22). 
Calorimeter  to  fit  boiler,  (49),  (32). 
Calorimeter  (use  overflow  can),  (49),  (52). 
Calorimeter,  polished  (use  overflow  cm),  (53). 
Candle,  large,  best  quality,  (54),  (61). 
Compasses,  drawing,  (56-58),  (61). 
Camphor  gum,  (63). 
Crucible  tongs,  (63). 
Emery  cloth,  (21). 
Filings  (iron),  (18). 
Funnel  (glass),  (46). 
Galvanoscope,  (20),  (21),  (22),  (30). 

Galvanometer  shunt,  adjustable  (spec.),  (see  Chap.  XII),  (24-26),  (29). 
Graduate  (500  c.c.),  (i). 
Graduate  (100  c.c.),  (9). 
Glass  pane  (9"  x  24"),  (43) • 
Gas  burner,  mounted,  (54). 
Glass,  piece  of  red,  (54). 
Glass,  piece  of  plate,  (57). 

Glass  jar  (quart),  (12),  (15),  (22),  (24-26),  (28),  (29),  (30),  (58). 
Glass  (four  pieces),  (red,  yellow, 'green,  blue),  (61). 
Glass  jar  (gallon),  (7),  (9),  (10),  (11),  (15). 
Hydrometer,  Fahrenheit,  (14). 
Hydrometer,  ordinary,  constant  mass,  (14). 
Hydrometer  jar,  large  (2\"  x  18"),  (14),  (64). 
Hydrometer  jar,  small,  (14). 
Index  (refraction,  air  and  water),  (58). 
Knife  edge,  wooden,  (39) . 
Linear  expansion  apparatus,  (48) . 


LIST   OF   APPARATUS  177 

Lead  shot  or  copper  filings,  (50). 

Lens,  double  convex,  (59),  (60). 

Micrometer  caliper,  (3),  (31),  (41),  (42),  (66). 

Meter  stick,  (16),  (31),  (38),  (39),  (42),  (43),  (45),  (48),  (54),  (55), 

(56),  (60),  (64),  (65). 

Mercury  (quicksilver),  (45).     (Numerous  experiments,  small  quantity.) 
Manometer,  open  end,  (47). 
Mirror  plane  (3"  x  8"),  (56). 
Metal  bridge  to  fit  quart  jar,  (58). 
Overflow  can,  (7),  (8). 
Pinch  cock,  (16),  (47). 
Paper,  tissue,  for  cleaning  glass,  (43) . 
Psychrometer  sling,  (53),  (desirable,  not  essential). 
Paper,  white  sheets  (12"  x  20"),  (56). 
Paper  section,  inches  and  tenths,  (62). 
Pins,  ordinary,  (37),  (59). 

Resistance  box  (i  ohm-ioo  ohms),  (23-32),  (34). 
Rod,  opaque,  supported  vertically,  f"  diameter,  (54). 
Rubber  bands,  (16),  (45),  (56). 
Resin,  (63),  (65). 

2  Revolvers  and  blank  cartridges,  (66). 

Sulphuric  acid,  dilute  (1-20  by  volume),  (21),  (22),  (24-26),  (28-30). 
Switch,  reversing  (mercury  contacts),  (24-26),  (30). 
Scale,  metric,  2o-cm.,  (i),  (2).     Useful  in  many  others  (paper). 
Sinker,  metal,  (n). 

Straightedge,  accurate,  desirable,  not  essential,  (56). 
Stopper,  rubber,  (46),  (47). 

Scale,  mounted  vertically,  (36),  (47).     (See  Fig.  n.) 
Steam-trap,  glass,  (52). 
Sal  ammoniac,  (52). 
Sodium  chloride,  (53). 

Screen,  6"  square,  mounted  vertically,  (54),  (59),  (60). 
Sonometer,  (65). 

Strips,  wood,  hard,  1.5  x  1.5  cm.  x  100  cm.,  (36). 
Scalepan,  spec,  (see  description,  Chap.  XII),  (36). 
Thumb  tack,  \  doz.,  (18). 
Tubing,  rubber,  burner  size,  (oo). 
Tubing,  rubber,  pure  gum,  i-inch,  (47),  (48),  (52). 
Thermometer  (-  io°-uo°  C.),  (32-43),  (46-53),  (64). 


1/8  PHYSICAL   LABORATORY   GUIDE 

Triangle,  draughtsman's  (3o°-6o°),  (2). 

Tube,  glass  Y  tube,  (16). 

Thread,  coarse  linen.     Many  experiments. 

Tuning  fork  apparatus,  (63). 

Tuning  fork,  large,  C,  128,  (63). 

Tuning  fork,  heavy  set,  (64),  (65). 

Tape  line,  100  ft.,  (66). 

Voltmeter  (or  volt  ammeter),  (33),  (34),  (35). 

Wire  gauze  sieve,  (18),  (or  bottle  covered  with  cheesecloth). 

Wire,  copper  (20  B.  &  S.),  insulated,  (19),  (31),  and  for  electrical  con- 
nections. 

Wire,  copper,  bare  (20  B.  &  S.),  (23). 

Wire,  iron,  bare  (20  B.  &  S.),  (23). 

Wire,  German  silver  (22  insulated),  (27),  (31). 

Wire,  soft  iron  (28  B.  &  S.),  (41) 

Wire,  soft  copper  (28  B.  &  S.),  (41). 

Wire,  hard,  drawn  copper  (28  B.  &  S.),  (41). 

Wire,  steel,  piano  (28  B.  &  S.),  (41),  (42),  (65). 

Wire,  steel,  piano  (22  B.  &  S.),  (65). 
Catgut,  same  diameter  as  22  wire,  (65). 

Wheatstone  bridge  (special  form;  see  Chap.  XII),  (27),  (28),  (29), 
(30,  (32). 

Weights,  set  (500  gm.  to  10  mg.),  (33),  (36),  (40),  (46),  (4),  (7-i?)> 
(47-49)- 

Wire-testing  machine  (desirable,  not  essential),  (41). 

Wax,  sealing,  and  paraffin. 

Watches,  stop,  (66) . 

A  SIMPLE  FORM  OF  VOLTAIC   CELL 

This  is  clearly  shown  in  Figure  14.  The  supporting  stick  should  be 
half  inch  square  cross  section  and  must  be  of  hard  wood  to  be  satis- 
factory. The  brass  screws  should  be  of  such  a  size  and  thread  that  the 
small  thumb  nuts  taken  from  old  dry  batteries  may  be  used  for  binding 
post  connections.  No  dimensions  are  given.  The  apparatus  may  be 
of  any  size  to  fit  the  jar  with  which  it  is  intended  to  use  it. 

I  have  found  3"  x  4^"  a  convenient  size  for  the  plates,  giving  an 
immersed  surface  of  about  3"  x  3".  By  the  use  of  washers  or  short 
pieces  of  ^-inch  brass  pipe  the  distance  between  the  plates  may  be 
regulated  to  show  variation  of  internal  resistance  of  the  cell. 


LIST   OF   APPARATUS 


179 


FIG.  14. 


i8o 


PHYSICAL    LABORATORY   GUIDE 


A  VARIABLE  RESISTANCE   GALVANOMETER   SHUNT 
This  consists  of  a  baseboard  4"  x  6"  x  1"  mounted  on  feet  made 
of  two  strips  of  2-inch  dowel  pin  each  4"  long.     Bore  holes  for  the 


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FIG.  15. 

binding  posts  and  mercury  cups.  Put  all  screws,  washers,  etc.,  in  place 
and  then  solder  in  resistances  and  connections  on  the  under  side  of  the 
board. 

The  resistances  are  best  made  of  No.  22  cotton  insulated  German 


LIST   OF   APPARATUS 


181 


silver  wire  which  runs  nearly  one  ohm  per  foot.  Relative  values  1:2:4 
for  the  resistance  coils  are  convenient.  These  used  singly  or  two  or 
three  in  series  will  give  a  wide  range  of  combinations  suitable  for  all 
kinds  of  work. 

The  actual  resistance  of  these  coils  will  of  course  depend  upon  the  re- 
sistance and  sensitiveness  of  the  galvanometer  with  which  it  will  be  used. 

Short  pieces  of  heavy  copper  wire  bent  to  connect  two  adjacent 
mercury  cups  are  used  for  short-circuiting  the  coils  when  not  in  use. 
See  diagram. 

A  WHEATSTONE  BRIDGE 

Select  apiece  of -board  about  8"  x  15"  x  i".  This  should  be  well- 
seasoned  wood.  Bore  holes  for  binding  posts  and  mercury  cups,  as 
shown  in  the  drawing. 


dx. 


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FIG.  16. 


182  PHYSICAL    LABORATORY    GUIDE 

The  contact  keys  are  made  of  strips  of  hard  sheet  brass  bent  as 
shown. 

For  the  ratio  coils  No.  22  double  cotton  insulated  German  silver 
wire  will  be  found  convenient.  It  is  desirable  to  adjust  these  coils  to 
exactly  one  and  ten  ohms  each,  but  this  is  not  essential.  The  author 
has  obtained  good  results  by  simply  measuring  off  lengths  of  one  and 
ten  feet  accurately.  The  resistance  of  these  wires  will  not  vary  greatly 
from  the  values  marked,  and  their  ratio  will  be  very  close  to  10  :  I,  which 
is  the  essential  thing. 

All  permanent  connections  shown  in  the  drawing  should  be  carefully 
soldered  on  the  under  side  of  the  bridge.  A  coat  or  two  of  orange 
shellac  will  make  a  neat  finish. 

This  apparatus  used  in  connection  with  an  ordinary  resistance  box 
(.1  to  no  ohms)  will  give  a  possible  range  for  measurements  from  .01 
to  1 1 oo  ohms. 

This  bridge  will  commend  itself  on  account  of  its  teaching  value, 
since  it  follows  the  theoretical  Wheatstone  bridge  design  very  closely. 
Another  good  point  is  its  low  cost.  The  necessary  material  need  not 
cost  over  seventy-five  cents,  and  the  labor  involved  in  making  it  is 
small. 

COPPER  TEMPERATURE  COIL 

I  have  made  a  satisfactory  coil  by  winding  fine  insulated  copper  wire 
No.  B.  &  S.  (Brown  &  Sharpe)  34  or  36  on  the  cardboard  cover  of  a 
thermometer  case ;  after  winding,  one  end  of  the  coil  is  fitted  snugly 
with  a  little  shellac  into  a  hole  in  a  flat  cork  3"  or  4''  in  diameter. 

Binding  posts  mounted  on  the  cork  and  soldered  to  the  ends  of  the 
temperature  coil  will  give  the  apparatus  a  neat  appearance. 

Finish  it  with  a  coat  of  shellac. 


A  HAND   SCALEPAN 

Cut  out  a  disk  3^"  in  diameter  from  thin  sheet  copper,  notch  the 
disk  at  diametrically  opposite  points.  Bend  the  wire  into  the  shape 
of  a  V  and  bend  the  ends  under  the  disk  and  solder  it. 

Make  the  whole  construction  as  light  as  possible. 

When  it  is  completed,  weigh  it  accurately  and  stamp  this  weight  on 
the  disk. 

This  apparatus  is  very  useful  in  laboratory  work. 


OALIPORNU  LIBEAET 
™IS  BOOK  IS  DU7o7THElASTl)ATE 


STAMPED  BELOW 


YB  66580 


251955 


<S 


